And I want to emphasize:
At level 5 according to RAW, most martials can shove up to 2x per turn. At level 11? Fighters can shove 3 times. Double both of those numbers if you use Action Surge.
However, in Larian's implementation they'll only be able to shove once.
If you think Larian's implementation of shove is too powerful to be a BA, you should want shove to be an attack-equivalent action.
If you really like shoving people, you should also want shove to be an attack-equivalent action*.
*This primarily helps non-rogue martials, but casters can Thunderwave to shove possibly multiple enemies and Misty Step to disengage as BAs, so they're fine.