@colinl8 -- You say you aren't familiar with 5th editiin DnD, so let me try yo put this somewhat into perspective. By the 5e rules, a shove/trip attempt can be made instead of a weapon attack when you take the attack action. Most characters only get one attack to make as part of their attack action, but martial classes get more, but at later levels than we currently have available in the EA (Nearly all martial classes get their second attack at level 5 for example).
As such, the capability to in the same turn both make attacks and shove is sort of a martial class feature, and making shoving a bonus action available to everyone deprives them of that profilisation much the same way making hiding a bonus action deprives Rogues of one of their class features. If we had more levels available to us than we currently do in the EA, we would no doubt reach the fifth level within the content already implemented, whereupon martial classed characters would be able to both shove and attack in the same turn, like you want to do. It would just be a feature of how characters improve with levels rather than available to everyone at level one.
I don't think anyone arguing against shove as a bonus action is doing it from a "realism" perspective. It's not about what you can realistically achieve in a turn, it's about the action economy, and the effects making shove a bonus action has on that economy in-game. Being a bonus action turns the choice of whether to try shoving from a strategical choice of whether to risk it for the possible benefit to a no-brainer, "always do this at the end of your turn" use. That's not fun design.
For example of how it messes things up: As it is now, even the AI uses shove to cheese the game mechanics. No, I am not referring to enemies pushing PCs off off ledges. In-game, there is a Help action. It reoresents a bunch of different action usage from the 5e rules, such as making Medicine checks to stabilise dying characters, or rousing sleeping characters awake. It costs a full action.
So say you use Sleep on a bunch of goblins and one stats awake. The way the Help action is intended, he could then spend his action to help one of his sleeping comrades up. But you also awake on being attacked, and shoving is a kind of attack, so the way the AI is written is that the goblin will instead bonus action shove his friend and then use his full action to attack as well. His buddy will awake and immediately run over and bonus action shove another sleeping goblin. This makes the Sleep spell (already heavily nerfed ingame) pretty much useless, and all because of how the action economy changes from making shove a bonus action instead of an action. And that isn't fun either.
As a bonus malus, it also puts you the player in the position of either having to similarly cheese the game mechanics when your characters are felled asleep or deliberately play it suboptimally -- when even the AI wouldn't do that if it had the opportunity.
And lastly:
If you don't like it as a bonus action, don't use it that way.
There's no other way to use it.
