the limit is in the words Attack Action, since you can only make one per turn.
That would be the case of the rule only stated that:
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.
That would mean that you can use attack action to make a shove and that would consume your main action - and that is how it works with classes without multiattack. That's why they follow with:
If you’re able to make multiple
attacks with the Attack action, this attack replaces
one of them.
If you have multiattack, shove will "consume" one of the attacks of the multiattack not full "attack action". That is not interpretation, that it what it says. We do agree that push replaces one of the attacks from the multiattack, yes?
It is in line with how attack is explained:
The most Common Action to take in combat is the Attack Action, whether you are swinging a sword, firing an arrow from a bow, or brawling with your fists.
With this Action, you make one of melee or ranged Attack.
Certain Features, such as the Extra Attack feature of the Fighter, allow you to make more than one Attack with this Action
See, it's structured the same way. Not all classes have multiattack so it is treated as exception, rather than a baseline. So:
Attack Action = push/grapple
Unless you have multiattack, in which case:
One of the attacks = push/grapple
