Without reading the entire thing I’m guessing its because Rush believes what he says and wants as many people spreading conservative ideals as possible.
Competition has little to do with it.
Rush does take time off. He does need someone to cover for him. He can't play re-runs the entire time. That it helps these guys to cover for Rush may have nothing to do with whether Rush wishes to help these guys or not.
I happened to listen to his response to a caller who asked Rush how he chose those who would cover for him. Basically, Rush said he merely looked for someone with a conservative outlook and who could competently do the job. He didn't mention anything about wanting to help these guys.