First off, since when has the word "Supplement" become a taboo word? You can't fit EVERYTHING in the dang core book. If WotC went to put every option, module, and sub-class into the PHB, the thing would be the size of a good encyclopedia set. The PHB needs the basics; a mountain-chopping warrior sounds right up there with a gish or an artificer in "niche" classes.
Second, Monk of a Different Stripe just means a warrior with supernatural abilities. Swap out a monks martial arts bent for traditional armor and weapons and turn his abilities more toward Western myth than Eastern mysticism.
I'm not sure how to respond to your poison quote. Are you saying that those who want mythic fighters are poison or those who refuse to allow it are? I don't believe either is the case, but if you think not chopping mountains in half is a poison to the game, I can honestly say this conversation is over.
I don't care about the mountain chopping itself. It can be more restrained than that. But there are those that have said it is "unacceptable" to have a fighter with even a touch of "mythic" characteristics, even in a supplement. Those are the people that are spewing poison, because they are basically trying to dictate the scope of the game to their narrow preferences. (That's why I went to some trouble to point out that I was no longer responding directly to your quote in that paragraph, but to a side issue.)
There are some good arguments to be made for not having particular elements on other grounds, but as these aforementioned people haven't made the slightest effort to make those arguments, I'm only mentioning it for completeness--and to note that that isn't a case of going after exclusion by itself that is the problem, but the reasons behind that exclusion.
No, you can't have every option in the main book. You
can have a good cross-section. That means that from the beginning, you need the various playstyles represented. If that means that each style is not complete, so be it. No playstyle should be a second-class citizen. That's my beef with, "stick it in a supplement." To often here it has been couched in terms of "stick it out of the way where it won't bother the rest of us."
And in any case, I'm not buying the "having trouble fitting it in the book" argument from WotC. (I would have from early TSR.) They have been designing systems that require bloat, sometimes so that they can fill out the page count. Hey, I'm merely trying to suggest how they can fill page count without it being filler material.
That said, I actually care more about the timing than the organization of the books. If, for example, they wanted to produce a "mythic" supplement right along the main playtest and development, and then release it as a different books, I'd have no problem with that. I want the effort made to do it right, and make early while it can still do some good. Not kludged onto the game after the core has already gotten locked into place and can't be tweaked a bit to make it work.