Such great info here! But some less helpful stuff, too, I feel, so I want to chime in.
Specifically, this idea that glycerine (glycerol) somehow "coats" your teeth and prevents mineral-rich saliva from doing its work on your enamel doesn't make sense. The reason is obvious to anyone who has ever worked with glycerine (which I have) - the stuff is *eminently* water-soluble and rinses *very* clean, very easily. It can be used to wash up hands or dishes, etc, and rinses off quicker, more easily, and more cleanly than any soap I've ever encountered. A drop of glycerine in warm water diffuses into the entire container almost instantly, even before stirring. Glycerine and other sugar alcohols (which includes Xylitol, I should mention, and it's extremely similar to glycerol) are not too different from simple soaps, anyway, and serve a very similar function in that they help make nonpolar oils and other compounds more soluble in water (aka, they clean stuff!). So assuming that you rinse your mouth after brushing (which I think everyone should), or even if you just rely on your own saliva, that glycerine is not going to be hanging around in any significant concentration unless your mouth is *incredibly* dry. A couple of swishes with plain water after brushing and your precious saliva's minerals will have no trouble at all reaching the enamel of your teeth.
I say this not just because "OMG someone is wrong on the internet," but especially because I feel that glycerine is a *perfect* base for many toothpastes! It's thick and gets nicely pasty when combined with baking soda, salt, herb powders, etc., and because it dissolves both polar and nonpolar compounds, makes a great base to extract the medicinal parts of any herbs involved. And of course, it also basically acts as soap, helping to clean the teeth and gums directly!
For my own mouth, after much experimenting, these days I use Weleda "Salt Toothpaste," which is the best I've found yet. I used to use the Auromere "foam-free" varieties (to avoid SLS) but I find the Weleda to be better (though different - perhaps the Auromere is better for gums and periodontal disease? The Auromere seems to leave my mouth feeling clean for a longer amount of time). Weleda products pretty consistently impress me with the appropriate herbs they use and the proper strengths that they're used in - the latter is especially rare in most mass-produced botanical products. Although in this specific case, that Salt Toothpaste has a lot of Horsechestnut and its extractives in it, which is a little scary due to the poisonings that that plant can cause, but I think those wiley Germans have established its safety, though I can't find much English-language research on the topic. The Salt Toothpaste also has myrrh and baking soda, which are great to have in there.
I really, really like baking soda as a tooth care ingredient because its high pH directly neutralizes the food and fermentation acids that are present in the mouth which cause tooth decay (cavities/caries) and contribute greatly to tooth erosion - especially from brushing! In acidic conditions, the enamel of your teeth is actually a lot physically softer than at other times, and this can mean that brushing can end up doing more harm than good (or at least more harm than it would in other conditions). That's why, these days, many dentists suggest that you don't brush right after meals, or at least rinse your mouth well before you do. By using baking soda directly when you brush (or perhaps a rinse beforehand, I suppose), the pH of the mouth is raised which makes the tooth enamel tougher and better able to hold up to the brushing.
One last thing I'll mention that I've found to be very helpful to me (and everyone I've recommended it to): The Dr. Collins "Perio" toothbrush. It isn't natural at all (sorry there), but it has a unique type of bristle that gets way, way in-between teeth and just clearly works much, much better than brushes I used before trying it. So give it a shot, if you get a chance, they're inexpensive and available in some regular drugstores and online. But yes, they are plastic.
Happy brushing, everyone!