Took a few un-paid as a middle- and early high-schooler, mostly to prove I was worth money and not a total fruit loop, which was probably reasonable at that age. Got paid after that.
Highschool coops are required to be unpaid to count as a credit in my province, so it is probably similar in some other places which would lead to that practice
School credit wasn't an issue; these were for my development and experience. I was homeschooled so I guess I could have put them down, but never thought to. It stinks that schools do it that way; I'm curious, to which province & nation are you referring?