Catholic vestments are derived from the every-day clothes of ancient Rome (with a few exceptions, for example the surplice originates from the Celtic alb). Originally clergy wore what was regular clothing, albeit their nicest set. Fashion gradually changed, while the Church retained vestments for various reasons. The cassock was originally a vestis talaris, a regular tunic worn every day. The cope has been mostly discarded by the Latin rite, except in Tridentine rite. But when used, the priest wears in when approaching the altar, in outdoor processions, and removes it when mass begins -- originated simply as a cloak, which is reflected in it's modern ceremonial use.
May as well ask why Scots wear kilts or Japanese wear Kimonos. Some traditions endure.