For the record so I can cut and paste in future threads on this, here's the arguments I hear against the mythic martials,
Assumptions--
no changes to spellcasting/spellcasters,
mythic martial will be a separate, new class
this mythic martial will be no more versatile and powerful than the current wizard,
all existing classes will still exist
"I don't want that kind of gonzo stuff in my D&D" -- retort: already there with the high level Wizard which is more versatile, reliable, and powerful than most fantasy figures. Its existing indicates high level D&D is gonzo/mythic land
"If you put this in, no one will play the current martials anymore" -- retort: ok, then we've found out what people really want to play and/or time to buff those classes as well
"This will make a broken high level game even more broken" -- retort: impossible. You can already play an all-caster party. And the mythic martial is no more broken than the Wizard. So same.
"If you put a class in that would add to the fun and enjoyment of a bunch of people but I don't like, it will ruin the game for me even if I don't have to use this class and it doesn't take away my current options which are just as powerful." -- retort: you are a bad community member trying to gate other people's fun.
"I don't want this in the core book" -- retort: fine. put it in a splat. I don't think this is a big issue for most mythic martial supporters
"You can't do these things without magic." retort: magic as in "fantasy" sure. The world is magical and fantastical so yes this is why the mythic martial can do things a normal earth human can't. These are not mundane heroes at high level. They have some origin that gives permission, with one option being you don't know. The specific type of D&D spellcasting doesn't need to be a part of it though (although you can use some of those mechanics if you want in design)
"You can't use X, Y mechanics in building the mythic martial so might as well use half casters. All limited use or narrative control abilities are spells anyway" retort: convention only. free your mind
"Making this class would be a lot of work and I'd rather design time spent on more adventures, another spellcaster class, etc." -- Retort: Somewhat valid but this would be a major gap filled for a segment of people and really make their day, so be nice and throw them a bone?
Others?