As far as I'm aware, classification only actually matters for certain Guild Order missions. They basically ask you to win with at least X number of Y type kamihime, or with at least 1 of every type. So yea, types were basically just vanity for nearly 1.5 years.

Oh, yea, some tower quest missions also ask for similar things. But there's only been one tower quest type event so far and it's been a month since.