I think everything works together on the hoof. The hoof wall, sole, and frog all offer protection to P3. They all bear weight.
Agreed. But I don't believe the walls are a *primarily* weightbearing structure, but they're mostly for protecting the rest of the hoof, from kicking rocks, etc. I think 'jammed quarters' etc are evidence of this.
They're extremely tough but they give under stress a lot easier than sole. That is why the frog does such a great job of cushioning and protecting P3. Natural concavity indicates that P3 is in a healthy and safe position in the hoof capsule. A concave foot, where the sole hugs P3, does a lot better job of protecting P3 than a flat sole.
The frog is mostly behind P3, especially the 'fitter' the foot - healthy, well functioning heels are big - and what's above the frog - the digital cushion, etc, should be the primary weightbearing structure, IMO.
I agree *generally* that some concavity is desirable & that flat soles generally go with thin, flared feet, but the presence or absence of concavity doesn't *necessarily* mean anything good or bad - you can have extra thin, nicely (naturally) concaved hooves, & you can have thick, strong, flat soles. I think it mainly depends on environment as to what's the most ideal in any given situation/horse, and *support* under P3 counts for just as much as protection - lack of support tends to lead to thinner, less protected hooves too.
Eg. Hooves that only ever work on pavement should
have their sole more 'filled in' & flat, as otherwise they'd have too little support underneath to spread the load. Horses who work on yielding ground however, can afford to have more concavity & longer walls, as the ground still allows distal support & reduces/stops the walls being peripherally loaded.