I, too, thought the capes would be explained further, as it does seem to correspond to the owner's magic. I wish they had been, since the audience would be able to then identify approximate magic types on sight, or be intrigued by a new, previously unseen color. Prime storytelling opportunities have been missed there.
There is only one girl I've seen who doesn't wear it, and that's Erika. There are multiple reasons to explain why she would not wear it.
1) She's the only Course 2 (Weed) girl character we've seen, so it may be a Course 1 (Bloom) exclusive uniform piece.
2) If it's truly based on magic, which does seem to play a part in the colors, Erika's style is sword and weapon-based where the other girls use a different type of non-weapon magic.
3) If it's completely optional, Erika has exactly the kind of personality that would forego the cape by choice.
As far as the texture goes, it's always looked like a sheer fabric attachment to me rather than lace. If it's supposed to be lace, they didn't do very well in animating it. Looks closer to tulle, maybe? Or, actually, my vote is for chiffon. Chiffon flows the same way as they portray in the anime.