It would seem to me that whatever you use should be what is best and appropriate for the sum of what the horse and rider need for optimum communication. Some horses do do better with a bit, some better with a halter. Some riders also are the same. There are horrific bits out there and some that are just enough to do the job. Halters are the same. I've seen ones knotted in such a way as to practicly rub a hole in a horse and others that were so badly missized that they could become a noose.
The one thing I have noticed is it seems that people on both sides of this issue think their way is superior for whatever reason. In my eyes, those people are limited by their prejudice and I have less faith in them to be open minded enough to recognize that sometimes, their way is just wrong when trying to solve a problem with a horse.
I've seen people who have trained horses their whole life do things with a halter or even a neck rope that bit people claim can only be obtained with a bit. I can't count how many times I've seen horses that were genuinely confused because the halter wasn't working for them or their owner. Neither is superior, only different, and ultimately only effective when used where it's needed by a horseperson who is actually taking the time to see what is actually needed for that horse and that person, in that circumstance.
Hopefully, all of us will pay attention enough to what is going on with the horse and rider that we won't have the ultimate goal of going halter only, bit only, or whatever, but what is correct for that combination.