The thing is, making these things use a limited resource allows them to be stronger and under the control of the attacker. Anyone can Shove (Athletics vs Athletics or Acrobatics) as long as they have a free hand, but it takes up an attack. The Battlemaster can make an attack that hits, and then determine both that they'll add damage and potentially Trip their foe, and doesn't need a free hand to do it.
3e had a number of combat maneuvers that were, in theory, open to everyone (bull rush, disarm, trip, grapple). However, in most cases there were such severe penalties for trying them without special training (in the form of feats) that you might as well not bother, and if you did spend the feats they became an expected part of your routine and not a Special Cool Thing to do on occasion. The classical example was of course the Spiked Chain fighter with Improved Trip, who would trip you at a distance, use Improved Trip to give you an extra hit, then hit you again while you were down with their second attack and 5'-step away, and then use an attack of opportunity to trip you again when you tried to close, and then repeat the process. That's just boring and exploitative