Those special attacks you describe remind me of Battle Master Fighter maneuvers. I've heard people complaining about the 5e fighter and wishing that the Battle Master fighter wasn't a sub-class, but part of the base class. Doing that would be a homebrew, but it might be less disruptive than giving bonus action shove to EVERYONE.
If they aren't interested in going in that direction, only allowing Fighters/Barbarians to do bonus action Shove, and making it an action for every other class would be better. Oh wait, they probably aren't interested in doing that either, because that would mean different classes would have slightly different UI's.
I am one of those people who likes playing the fighter class but who hates that the fighter does not have anything to do that makes them unique like all the other classes. So I like these ideas!
