Yeah I'm... really not seeing how any of those are a problem. Every single one of them is simply a mechanic for gaining a bonus attack... and making attacks is kind of a core thing for initiators. So I'm not sure how an initiator "can't use them".
Guess you could argue you'd rather boost, but that's not unique to initiators either.
Mythic Initiator stuff certainly could be a lot of fun, I don't disagree there, but I'm not seeing anything that you "Can't use" with a path of war class, or even anything that really conflicts with your abilities as any of those classes.