First of all, as LindaAd said, its a question of safety. Good luck trying to control a horse who spooks without a bit.
Secondly, you cannot actively teach a horse to go on the bit without a bit Maybe it would be possible if the horse actually was a confirmed dressage horse who carried himself, but if it was a green horse? Nope. (but I guess this is only important if you wanted to ride in that style)
(not trying to cause a fight here, honest )
But I actually had MORE control in a bitless bridle and had better brakes in one too, should the horse spook.
Also, you can actually teach a horse to go 'on the bit' with a bitless bridle. Although they have no bit in their mouth, they can still work from behind and work in an outline. Milly learnt to do all of that in a bitless, I and I hacked her to Royal level (the top level of showing here).
So yeah, there are alot of misconceptions about bitless bridles and I just thought I'd share my experience with you