Many years ago, at least in the Islands, broncs were horses that---yeah, bucked! If there was NH-type starting of horses, it wasn't well-known, so there was always a supply, I guess, of breaking-horse "failures".
I took lessons at a small place leased by a Marine and family, and there was a Marine rodeo every week back at the base, or somewhere, I don't recall. Anyway, when the horses didn't buck any more so well, they were sold off VERY cheap. So now you know where a lot of our school horses came from!
I'm glad they're now being bred for it. I'll say this, all those horses could jump. We didn't go high, but thinking back, and I believe they enjoyed it.