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.