I used not to do much appearance customisation in games because it didn’t feel as important as in a game where your character is visible onscreen. But I’ve slowly been increasing it over time. Some players are really into the game responding to how tall they are, so more recently I’ve been including that for referencing when hugging someone, or if a character is reaching up/tilting the MC’s chin, etc. It’s not something that really matters to me when playing, but if players enjoy it I figure I may as well.
In Noblesse Oblige I went into more detail than I had before, referencing what the MC does with their hair before going to bed, and lots of beta testers responded really well to that which was lovely. As the game is about being fluent in another language, I gave the MC the ability to define how they learned the language, and that’s referred to through the game. Then there are things like how the MC ended up in their current situation, different outfit choices for different situations, their family relationship before the game starts… because of the game being shorter, it was important to me that the MC had a lot of chances to be self-expressive and that the game was responsive to it.
The problem you can get is with integrating options (especially appearance choices) into a game in a way that feels natural. There are a lot of threads on that subject, with a variety of approaches. I haven’t quite figured out a way that feels completely right for me as an author; I don’t like when those kinds of choices slow the game down, but there are only so many ways of describing the MC’s own appearance. Rarely does someone in real life think “I’ve got brown eyes” without prompting or context!