Shove as a bonus action" at first sounds apparently minor, almost trivial.
"Oh well, it gives you a chance to make an additional attack for round. It gives my characters more things to do, right? What's the big deal?"
But then over time you realize it makes shove surprisingly convenient to use over and over, rather than "situationally useful", since as far as bonus actions go there's only rarely better options.
As a result, Larian's own systemic AI learned over updates to spam shove constantly: to push characters down precipices or buildings, to push characters on traps or damaging surfaces, to wake up allies that were put to sleep with a spell (something that normally would require an action of some sort), to create distance from the enemies and not incur in attacks of opportunity, etc, etc.
The aggravating factor is that shove is not even limited to push an enemy five feet away (or down a precipice when standing on its border) as it should be and instead it's occasionally able to YEET characters few meters afar.
As a result, not only it's a surprisingly convenient bonus action to use, but its potential effectiveness as a "1 hit KO" is exponentially increased. Normally you'd have to worry about sitting too close to a precipice (or a lava pit or whatever). Now being anywhere in its vague proximity can turn into a suicide.
Knock on effect on the balance aside, this also severely affects the "vibe and mood" of the fight: what should be a battle of sword and sorcery turns occasionally in a clownfest of people goofing around pushing each other at any given chance.
Going to mention a couple things I had to go through at the goblin fight when first arriving at the Druid Grove that exemplifies why bonus action shove is absolutely insane.
1) Enemies were using bonus action shove to wake each other up if they were afflicted by the sleep spell.
2) One enemy walked up to my Bard and KO'd them, then shoved them into a fire field. With one standard action and a bonus action, they managed to push them out of range of closer range healing spells, AND immediately score 2 instant failed death saving throws from height and fire damage. If my Bard's turn was next in the initiative order, he would have immediately died before I had any chance to do anything about it. And this is from a level 2-3 enemy barely 1 hour into the game. Spells, which are a limited resource, don't even come close to doing anything like this until maybe level 10+ (and that's a low estimate), if at all.
I mean, sure, you can do all this yourself too, but with the action economy skewed against the party as is during many encounters, it has the potential to evolve into something that's more effective against the party rather than equally taken into consideration for players and enemies. Such amateur JRPG-level design is precisely why a number of people here are very concerned about it.