Making shoves an action would make it a right PITA to actually control space and not simply get overrun by the relatively large amount of enemies that we're going to face every so often, which is presumably the main reason Larian made that little house rule change.
And I don't really mind that, to be honest. AI can do it to us as well, after all. But shoves obviously should not send people flying like they're shot out of a cannon. It seems very much like there's no change of horizontal speed until the victim of a shove has stopped falling. If that's 50 feet below then that means the character flies literally 100 feet away, which is nuts.
Short version, don't "fix" shove by letting it remain as nuts as it is and turning it into an action, fix it by letting it remain a bonus action but tone the shove distance down significantly.