I think encouraging players to utilize verticality and push/pull people off ledges is definitely part of D&D. It's not just a DOS2 invention. There's more to D&D than just attacking with your weapon. The game rewards creativity, especially if you have a DM that is any good.
That said, the rules should more accurately represent D&D 5e. Not being a bonus action is probably a good start. That's what made pushing attack so good for Fighters. You could hit a target AND push them at the same time. Now you just get an extra push.
