It's definitely possible to "not bash into walls"
You don't always need to have bespoke animations- sometimes keyframes and realistic constraints can get you there. I think Unity is working on a framework for natural human animation.
David Rosen pulled off quite a few little masterpieces -- his gamedev competition entries always had fantastically unique aspects. I cannot believe "Black Shades" was almost 20 years ago! (I have no affiliation, but I am glad to see https://www.wolfire.com/games is still alive and kicking!)
Lugaru and later Overgrowth have been the outcomes of what can only be called a decades long obsession with getting the player controls just right, allowing very natural and responsive control and movement, through creating emergent behaviors from first principles, resulting in a rich and natural interaction with the environment (and other characters, see the fighting mojo), in contrast to the many, many AAA titles that just constantly break the immersion through unnatural, jarring behaviors and frustrating limitations.
It's significant too: nothing frustrates players quicker then controls feeling "unresponsive" by doing something that's different to what they instructed.
Which is what some game does fundamentally bad. When using skills in some game. Your action got locked completely and won't respond to your request until animation finishes. (And when the mob hit you in the middle, you can't do anything because animation is playing.)
But some games makes more efforts into these and allow you to transition to another action in the middle of one, blend them seamlessly or even play them at same time. That makes the game feels much more responsiveness and enjoyable. Feels you are actually moving your body instead a online character with high action latency.
I seem to recall the game "Bound", where you guided a low-poly ballerina through fairly abstract levels, had a really nice solution to "people don't bash into walls": if you tried to guide your character into a wall, she'd just start doing some stretches against it, which feels pretty accurate given how I tend to behave when I'm attending dance classes regularly. :)
Other characters might do different things; a mopey teen might slouch against the wall, a gun-haver might press against it and peer to the side, looking for cover, etc.
Obvious reasons not to do this start with "oh great, one more thing to add to the character state machine and debug" and "oh great, a few more animations to fit into the budget". Maybe also "it stops feeling like you're controlling the character". Someone whose day job is video games probably has at least a dozen more reasons, possibly even stories from when they tried it and abandoned it.