It's more about immersion and allowing players to add a little bit of extra veneer to the story they want to experience. And I wouldn't entirely discount the impact of this from the player's perspective.

That said, the extent to which customization needs to be offered to achieve an appropriate level of benefit can vary. In Pathfinder: Kingmaker for example custom character portraits and a basic level of customization for the 3D model was absolutely sufficient. In the Avernum series, pretty much the same deal (though that didn't have built-in support for custom portraits).

In something like Skyrim though, where the level of visual detail and interaction in the world is pretty high, I'd have the same level of expectation for what I can do with character visuals. And then of course there's games where I'm perfectly fine with playing a pre-set character or a "no-name" character in general, like in the STALKER series, Half-Life, Dishonored, etc.

It all depends on the kind of game experience you're aiming to create and what kind of story you're trying to tell.