Why don't they just put the current Shove on a Feat? Then it can stay and people who want to use it can use it. There are plenty of Feats in the PhB that are barely used or underwhelming, putting this on them would make them much more viable. I do still think it needs a nerf but then we can appease everyone. Strength characters like Barbarian and Fighter could use it, Dex characters can ignore it, along with classes that already get it through mechanics (Battlemaster, Monk, ect.)
Tavern Brawler is a great candidate for it, as there is no grappling yet and the feat was always underwhelming. Athlete is another good one.
