what happens if riot made it so we could only queue for one role?

You mean teambuiler? that took forever if you remember

Queue times would be slightly longer.

But people would be way happier in general.

Queue times will be ridiculously long.

Longer Queue times because there would be less people willing to not just support, but practice off-roles in general. I think a decent solution would be allowing but not Forcing people to queue for a secondary role.