If anything, it's zero cost and more uses. This is only compounded by the shove distance being insane.
Saying a bonus action is zero cost is an obvious exaggeration, sure, there will be times in which your characters won't have a good opportunity to use their bonus action, but bonus actions offer options beyond pushing people. Also, if shove is an action you will be able to attempt to push more people per turn because, as I mentioned earlier, so far there are more ways to get additional actions than bonus actions.
I don't think you quite understand how the effect of an ability vs the cost of the action are two separate things.
Come on, be reasonable, sure, I shouldn't have said "... if you fail" because the cost is the same regardless of the outcome, but my point is that an action is generally more valuable than a bonus action and thus has a higher cost on your action economy.
Having it as a bonus action means the effect of Shove is always available for everyone one every single turn. There is nothing to think about except in the extremely rare circumstances where you want to us a bonus action for a different ability.
The circumstances in which your bonus actions are valuable may vary a lot depending on your class: a berserker, a rogue, a monk and any dual wielder all have good uses for their bonus action that they can use pretty much every turn. The best outcome a shove can have when you really have nothing else to do is a free disengage, because in the situations where pushing an enemy could make a significant difference, it would also be worth sacrificing an attack action for, and like I said, there are more ways to achieve additional attacks than additional bonus actions.
Again, I'm fine with either ruling, I just wanted to bring a couple points up because I didn't think the discussion was judging fairly some aspects.
