I love in depth character customization for RPGs for the same reason I like dialogue options that let me define my character's personality. Making a character that's visually, "my character" is every bit as important as fleshing out who they are beneath the skin, because how they look can say things about who they are. The condition of their skin, their apparent age, how they keep their hair, the coloring of their hair (factors into age), how they treat their body and thus what sort of shape they're in, scars, a missing eye or blinded eye (with scar through the eye to match), tattoos and much, much more all can say something about who your character is. The things they've done, seen and experienced can be conveyed through even very minute visual aspects.
This isn't something I do for the game, or for other people out there, it's for me when I try to come up with an idea for a character. Building the character visually helps me develop who this person is, and how they're going to act, in my mind, before I'm ever allowed to say a single word or perform a single act with them in game.
As a result, character customization (statistical and visual) are some of the most important things an RPG can bring to the table. I view character customization as equally important to gameplay, writing, dialogue, choices, consequences, gear, leveling mechanics and pretty much any aspect of a game. I don't really view any element of an RPG as 'unimportant' or 'lesser' they all have their very real value and importance in my mind.