All interesting ideas.
Here is a big long wall of text, on a few different points.
If you want to skip to the end:
For "before the bathroom" traditional floor options, look at kitchens, cheeserooms, and similar designs.
Think 'washable,' not necessarily waterproof.
Replacing a little grout now and then might be easier than waterproofing an entire floor.
Modern earthen villages:
I have visited a few villages in Morocco, and some urban bathrooms too.
Earthen floors, the traditional way, do make a lot of dust (always sprinkle water while sweeping), and I am told the village women 're-do' the floor about once a month (moving all the furniture and re-finishing with fresh clay/paint, maybe this is no more work than mopping and waxing a high-end floor, but it sounds like a lot of work to me and to the translator who described it to me).
In bathrooms, it is common to use stones, tiles, or concrete, anywhere from just a few stepping stones, to going up the walls as high as your budget allows.
It is also common to have an
outhouse in the villages, or to locate bathrooms near the "outdoor" or "public" parts of a building.
Some homes have the bathing room and toilet indoors, some still have it outdoors across a courtyard. (the whole home is rooms around a courtyard, it's sort of indoor-outdoor living, warm climate.)
The common attitude seems to be that the whole floor of the bathroom, like the outdoors, is "dirty," you take your outside-shoes off before coming into the "nice" part of the house.
These areas use a squat toilet, it is not a place you want to stand in bare feet. When I did not bring them, I was offered someone else's 'bath-shoes' (flip-flops, two-strap sandals, or plastic "jelly" shoes if you have girl-size feet).
In the homes where the same room is used for bathing and toileting, and the toilet serves as a shower-drain, you wash the floor a bit while heating the water for your shower.
And you shower with your shoes on.
In the US Southwest, my sister and her husband live in a modern adobe house (maybe 1970s or later). They have fully modern detailing; I don't know if the adobe walls are stabilized with Portland cement, but the interior detailing is very conventional/modern. Almost all the floors are porous Saltillo tile (he re-did them after they moved in), and the bathroom floors have sheet linoleum and little washable rugs. They have 2 kids, small enough that they use a stool to get up to use the sink. Their kids are pretty well behaved, they usually don't make more water on the floor than you can collect in one finger-thick bathroom rug, and maybe half a towel. I would suspect these bathrooms have cement-board and waterproofing behind their linoleum, but in any case, the climate is dry enough that the water will generally evaporate before it makes any mold.
Cold-climate traditions:
In England, even before indoor water-closets, there were common designs for well-drained cheese-rooms and dairies. These often had tiled floors so they could be washed down. However, the tile was porous, so it would maintain 'cheese culture' and humidity, like a cave. The milking barn might have cheaper versions of the same idea - stone cobbles for the floor, with a gutter, to make it easier to wash it out.
Kitchens:
Kitchens are also designed to handle a lot of spills. (So are breweries, pickle-factories... maybe there are
local industries with long traditions of washable floors)
What are the traditional kitchen floors for your climate?
Some places have a culture where the kitchen and 'scullery' are almost outdoors, out back.
Other places, these are heated rooms, and designed so that spills can be cleaned.
Some places, the traditional kitchen was sort of an indoor barn, with earth floor and even
straw on it, an easy place to start a grease fire, and not very sanitary.
Some places made the kids white-wash the kitchen and
dairy regularly, slowly building up a layer of mold-resistant and washable wall surface, painting over any spills that would not wash up.
Modern natural options:
True linoleum, now sold as "marmoleum," is a blend of linseed oil, granite dust, fibers, and other stuff like that. (May include cheaper oils, other kinds of rock dust, pigments, etc.)
You can make an "earthen" or "lime" floor that is essentially very thick linoleum, incorporating oil into the final finish layers and then oiling the surface. If you work very hard to burnish the top, and oil and wax it regularly, it might wear almost as well as commercial marmoleum.
However, it is probably cheaper and easier to get a sheet of real linoleum, and install it over a nice smooth sub-floor of any convenient material.
I agree about earthen floors being possible to waterproof, but difficult. Clay likes water better than oil; it will hydrate and soften eventually, unless you are VERY good at maintenance and the floor has a thick layer of wax at all times.
If you are going to use 1/2" to 1" of high-quality drying oil like linseed, plus regular waxing, I don't personally see much difference to buying a commercial, natural "plastic" like linoleum, that will be easier to maintain with less wax.
Boats:
The other traditional environment that required waterproofing was boats, and these were generally caulked with oily mastics (white lead and linseed oil, for example, now we might use something other than white lead), and then painted with pitch or tar for waterproofing. The wood would also swell with water under constant exposure, maintaining pressure on the caulk, but this hopefully is not the conditions for your bathroom.
I include it only to give the example that we have been using expensive 'natural' plastics, like bitumin and pine tar, for this job for many centuries.
Tile and Stones: Glazed tile, or water-resistant stones like slate, will help water run off toward the drain. High-end bathrooms and entertaining rooms from Roman times use tile mosaics set in hydraulic lime; high-end modern bathrooms often use semi-precious stones. In some cities, slabs of marble can be gotten from building repairs in older buildings for fairly cheap, and maybe 3 to 5 panels would cover most of a bathroom floor quite well. For laboratory sinks, soapstone was used (it is not as susceptible to acid as marble).
Why do you worry about the grout? Have you seen problems in other areas where you tried to lay tile?
I've bathed in a lot of rooms with a few broken tiles. The grout is mostly for keeping the stones from moving; it can be waterproof, or not, but in any case it is not a large portion of the surface.
You can do a tadelakt treatment on the grout, and burnish it. (Lime grout burnished with soap before it's done curing.)
Or oil and wax it, over lime or whatever grout you prefer.
You can sink the grout lines and use them as tiny drainage channels, or keep them level and wax over them to encourage the drainage to find the proper channels.
The goal, over all, is to make it easy to move the water down to the drain. But it doesn't have to be perfect.
You can encourage the water with a little sweeping, or mopping, or using the dirty towel to sop up the worst mud.
Then you just need a floor that doesn't actively fall apart while you are dealing with the mess.
I think washable is more important than waterproof.
Natural materials aren't perfect (like the welded stainless room). But they can be good enough.
Under-floor drainage:
Yes, you could collect the water to a pipe.
Once you have a floor that you can wash (linoleum, tile, stone, or waxed material), you have a choice of moving most of the water to a floor drain (probably by sweeping, mopping, or squeegee), or removing it with towels and wringing/draining them in the sink or laundry.
To drain the floor, the pipe clearly must exit below floor level.
(Remember floor level is adjustable - if you have to, you could build a step up into the bathroom, building up the floor above the level of the available drain outlet.)
If you have already got running water in the house, you should have an outflow drain somewhere, and you may be able to install a floor drain that connects to this, to the main sewer, septic, etc.
But for something like bathwater, which is at least as clean as the outdoors most of the time, you could also do a greywater drain directly out to somewhere convenient.
I agree that doing floor drainage on the surface is easier to inspect and maintain. Bath-mats or towels on the floor is the most I would want, myself.
The wooden bath-floor idea is common for saunas and outdoor showers. For saunas, it's generally an adult room, and the heat and cedar make for quick drying and low mold problems.
For outdoor showers, the wood floor is just convenience because standing on loose stone or gravel (or mud) is not comfortable. These are not areas where people worry about inspecting - they use it, eventually it rots or falls apart, and then they look and say "oh, gross." And they either move it to another place, or replace the funky gravel and re-build over "clean" drainage gravel again.
The building should already have sub-floor drainage for its foundations, like gravel. But this is not always the case.
I agree, I would not want to pour a lot of bathwater down there and hope.
So we know we want to remove most of the water, and that we are not perfect.
The "residue" of the water - where will it go?
There are three answers:
- "away" by drainage and/or cappillary action (sub-floor through gravel, directed toward the outside of the building; becomes ground water.) Small amounts of water will never fully drain - they will stick to surfaces, especially layered materials.
- "away" by evaporation (good ventilation can dry the floor; porous materials can wick water away from the back side of water-resistant surfaces; bathroom fans, heat lamps, underfloor heating, etc. can all help evaporation);
- or "nowhere." This can create mold problems. Mold can be controlled somewhat by good ventilation; by temperature; by choice of material (lime and stone are more mold-resistant than clay and fiber); and by washing/drying the surface promptly.
With the same sand-and-brick process, only using non-porous stones instead of porous bricks, you could have something almost 100% natural, and stable enough to support a soft grout of linseed-lime mastic, or linseed-sand.
I think if you start with the idea that the floor is washable, not necessarily 100% waterproof, then you have a lot of choices of natural materials.
If you start with the idea that you can let the kids play "tidal wave" in the bathtub and never clean up, then you are going to see some damage to almost any materials you use (natural or synthetic).
All materials wear out, and need maintenance.
and since we're comparing stories:
My personal bathroom right now is built inside a wood frame, with wooden sub-floor, with little "throw-rugs" of salvaged marmoleum and bath-mats. And a shower that has its own drain pan. I have cut a piece of linoleum to go around the toilet, but it's not sealed in place. Because the bathroom is raised up in the wooden part of the house, it is easier to drain the toilet, sink, washing machine, etc.
We have been over-complicating our thinking, wanting to lay some floor-heating under the finished floor, which has delayed our progress in even HAVING a finished floor. So there are sometimes spills which have to be cleaned up, or which contaminate the wood.
I used a 'natural' paint on the drywall ceiling, and there is no ceiling fan, and I am starting to see mold lines near the joists (coldest areas; between the joists the ceiling is insulated).
There is a particular mold here that loves to eat drywall if the temperature is cold enough, and I think the bathroom gets cold enough for this mold to flourish when we are gone for winter holidays, fall or spring work trips, etc.
I had good luck in a previous moldy bathroom using a paint made with lime and borax-and-casein, no clay; it did not re-grow mold for almost 3 years that we lived there after first trying it.
So i may do that for my ceiling, after installing a proper vent fan.
Not perfect, not by a lot.
But it does have the nice little 'cabinet with all the valves in arm's reach' under the sink, as you describe.
And it is way more comfortable and convenient than an outhouse, in this cold climate.