I played football in junior high school in the mid-'80's, and jockstraps were never mentioned at all. Neither were cups, for that matter.
We were each issued a full set of football equipment, but undergarments were simply not discussed. Absent any real notion of an alternative, I just wore a pair of briefs under my football pants, and it was never a problem; I'm pretty sure that's what just about everybody else did, too.
The first time I ever handled a jockstrap was in college, in 1989. My school's gym had the policy that anyone using it (for P.E. classes, lifting weights, etc.) had to be wearing a set of the school's gym clothes: Upon check-in you were handed a basket containing a cotton t-shirt, shorts, a pair of socks, and a jockstrap. Since they didn't actually check undergarments of users, you could wear whatever you wanted underneath in practice. However, I sometimes wore the jock just to avoid getting the briefs I'd worn over there sweat-soaked. It felt kind of strange, and my shorts would sometimes get stuck in my butt crack.
I've played soccer and basketball through the years, and have always simply worn briefs. I'm now a recreational runner, and usually wear purpose-built running shorts that contain a liner for support - they feel comparable to briefs, as far as amount of support. I don't own a jockstrap and have never worn a cup in my life.