considering a natural build

We're moving soon, probably to property with no house, and I'd like to make something with alternative methods (we don't have much cash, to be honest) Probably earthbags.
It looks to me that the most expensive part of building with natural methods is when you try to put a traditional roof on it. So, my thought is to cut out the need for traditional roofing by doing something like this:

Is there anything about this design that would present problems, either in building it or over time? Will earthbags be ok in this configuration? Or should I just do earthbags for the vertical walls, and perhaps cement bricks for the arches? I've heard some people say that traditional stucco is what they use for domes, so I imagine that's what I'd use for the entire exterior?
Location would be east Texas. Not sure particularly where, we're still hunting for that perfect plot of land.

A design like that is guaranteeing that the entire surface of the house needs to be completely waterproof, and any rain will run across the whole surface and into the ground right at the base of the walls. In a dry and warmer climate, that may not be an issue, but in colder and wetter areas, it would be a recipe for early failure.

Ah, I had considered that the structure would need to be entirely waterproof, but it did not occur to me that all that water has to go somewhere...Which ends up right at the foundation.
I have seen geodesic domes built in very rainy areas--how are they dealing with the water flow directly to the base?

Any water flow off the building can be dealt with, but it MUST be dealt with.  In this case a rubble trench with perforated drainage pipe running downhill and then open to daylight (but screened to keep out rodents and insects) might do the trick.  That said, Earthbags would be better in round buildings, slowly built inwards to a true round dome, which is much stronger than an arch.  Doing this with a rectangular building with a steady arch, as your drew, would be a lot harder and potentially very bad if you did it wrong.  A reciprocal roof (google it) might be something to consider, but from my understanding, there is no real issue with putting a regular roof on a bag wall, so long as your put a solid beam on the top of the wall.  You can do this with a number of different methods, including concrete.

One rule that new builders should always consider is that any house lasts far longer with less issues, if it has good boots and a wide brimmed hat.  Focus on having your foundation dry, and your roof overhang as much as possible (considering you light needs), so that you do not have issues with water on your structure.

Thanks for the input. I figured there might be a reason I hadn't seen this particular type of building before, but I thought I'd get some advice anyhow.
I like that reciprocal roof, it makes me think of a rather flat teepee (lol)Does it work only for perfect circles, or are other shapes possible? (oval, ellipse, etc)

I have not built a reciprocal roof, but I understand that they are very forgiving for shapes.  I was just introduced to the concept this year and looked at a lot of them online, some are spirals, and amoeba shaped.  There are plenty youtube videos, some of them with good details on how to build it.  Relatively simple (no major skills required), just follow the basic technique.  Putting up a single temporary stabilizing vertical pole, start laying the initial pole, and bolt the next one onto it, leaving an open circle in the center top.  The vertical pole is removed at the end.  There are ways to make the finishing log easier to put in, such as using a ratchet strap to close the gap (if there is one) between it and the first pole, and it is advisable that a person screw a ring bolt into each pole near the end, or just inside the wall, and run a cable through these, which keeps them even more stable; the same can be done by drilling a hole through each of the logs. Additional logs are laid in each gap and then roofing is put on.  All of that can be found in a couple hours of watching videos and reading online from Uncle Google.   I can't remember all the details of how many poles are recommended to build the structure.