If people cant create games when they want like on safelist then soon you will get same amount of games like on safelist. Maybe there are better games there but they happen few times per month.
I'd honestly recommend you to just drop the competitive spirit and just play for the sake of fun, forget that PSR is a thing and keep in mind that winning, losing, stats, PSR, none of it matters. Then again, if you really want to stick to your idea, I guess that the closest thing to it would be the old Dotalicious-Gaming system, ones who played on DLG back in the days will most likely relate to what you're trying to say.
i never played on dotalicious, can you explain how it worked?