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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.
Sure, maybe you didn't mean to go that far. But, I still think the core argument stands, making Shove a standard action forces choices while a bonus action cheapens the action, making it where it should just be used because it's free, except in situations where a bonus action can be used.
I think other arguments is that it also steps on other Feats/Class Features in the game that allows players to Shove as a bonus action.
The other stuff that others have mentioned is Shove moves a character much, much too far. Maybe this isn't as bad a situation if it really only moved 5ft, but I am only going to go with a maybe.
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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.
I always viewed the issue with bonus action Shove as a way to control/disengage for free for any turn you can't/don't want/choose not to some other bonus action instead. It's effectively free for no draw back. That normally requires a class balance Feature or spending a Feat to gain something like this, like Shield Master, Charger Feat, ect.
