I am fine with any new class (well maybe any except a Warlord, I don't want another one of them).
I am fine with a more powerful Mystic Martial. I am fine with a new caster class that is even more powerful than a Wizard or a new caster less powerful than a current Wizard. I am not fine with changing the current classes, nerfing the current spells or buffing the current fighter in a fashion other than giving it spells. Most of the classes that exist now need to be available at their current power level and with few changes IMO.
This is position that is easy to work with and can make a lot of folks either happy or fairly satisfied with a "consolidation prize" (e.g., they really want spellcasting nerfed but if not...)
I would disagree with the assertion that many who complain about the fighter being weak would be ok with a new more powerful mystic martial class. I think they would be upset that you made that class instead of buffing the fighter. They would say that there is yet another class that is more powerful than the fighter and that the balance is worse and the Fighter needs to be brought up to the same power level as the Mystic Martial. They will say the same things about the Mystic Martial being too powerful much like they are currently saying about the Wizard being too powerful.
At the end of the day I think there is a small minority of players that want a more powerful fighter but don't want that power to come from magic. I think there is a small minority of that small minority that would be satisfied with a new class that accomplished that.
Maybe, it's about the assumptions and context about what else would or would not change though.
It's true, there are a bunch of people that think the Wizard is too powerful and want it (and spellcasting in general) nerfed.
IF that happens or is assumed, then there is a whole different discussion on what martials should be depending on what spellcasters look like.
A bunch of those same people if presented with the assumption that spellcasting/Wizards will NOT change, would prefer there be an equivalent high level martial -- call it the Mythic Martial.
I'm in this camp.
This is what I am talking about in the post above. I think there are a lot of people who will be upset with a 2nd more powerful non-casting, weapon-using martial and will not accept a Mystic Marital because if this.
I don't know if this is a lot of people. But this is definitely the "it must be my way and even adding an optional class that I don't like will ruin the entire game for everyone..." stance that is frustrating.
I haven't seen any good arguments against an optional class (while keeping the existing Fighter).
You can ban it at your table if you as a group don't like the aesthetics of it, or if it's not banned and becomes really popular than I guess that is what your friends wanted to play all along anyway, right?
Personally, I think the reason we don't have a Mythic Martial is a personal preference of some designers, inertia of history, and a lot of causal players that play lower level and are ok with the current Fighter because it works ok at those levels and there isn't any alternative presented. Combine that with a somewhat more difficult design process and it becomes not worth it for them.
That said, I also think that if this Mythic Martial was presented as an optional class that it would be quite popular with the causal player (and others), and actually increase the popularity of the game.