It might me an interpretion issue but if i read the PHB i do read there that you can shove once per turn.
PHB says:
Quote:"
Sh o v in g a C r e a t u r e
Using the Attack action, you can make a special melee
attack to shove a creature, either to knock it prone or
push it away from you. If you’re able to make multiple
attacks with the Attack action, this attack replaces
one of them.
My understanding is that means you can replace any attack with shove, rather than replacing
only one attack with a shove. See, eg,
this tweet from Jeremy Crawford. But I agree that it’s somewhat ambiguous. Perhaps there’s a more definitive ruling somewhere?
I’d still prefer shove to be an attack action, and deal with potentially multiple shoves from warrior types at higher levels rather than multiple attacks plus a shove, but regardless of whether shove is an action or bonus action, agree its distance needs to be reduced.
