I've been folding my sensei's hakama since a few months after I began training. I think I started by Sensei and a couple of other people saying that it would be good for me to know how, and I asked a sempai to show me how to fold it, and then I became the primary folder of the hakama.
I think it's an honor to fold the hakama. It shows respect and appreciation toward Sensei or sempai.
I get the feeling that a lot more female students fold their Sensei's hakama than male students, at least in my limited observation. I wonder is there a different philosophy from a female/male perspective.
Personally I look at a Hakama as a tool or part of ones equipment and I've always been taught to look after your own "stuff" so to speak.