The problem is there exists a version of Quake Champions where everybody plays equally. It's called Quake 3: Arena.

The thing is, Q3A was originally supposed to be a sort of primitive hero shooter, with the various characters falling into different classes: fast, lightly armored "light" characters, more robustly armored but slow "heavy" characters, and a class in the middle. This was scrapped before release.

Well, a lot of it found a home in Team Arena, but that wasn't particularly well received.