If she doesn't want to listen or she wants to bolt, nothing on her face will stop her legs from moving. Bit = control is an illusion. Bitless = less control isn't true either. I believe my rope halter is harsher than a snaffle bit. I have better "control" with it than I do with the French link I use when I need a bit.
So I ride bitless for the simple reason that my mare likes pressure on her nose more than in her mouth. Mouth pressure makes her lock her jaw and become tense all over. She also eats and drink better in competition without a bit.