For all intents and purposes, right now COVID in a particular area is either going to be 100% a single variant, or a variant in the process of outcompeting another variant. There hasn't been a situation where there's been equilibrium between multiple variants that I'm aware of.

Also, there is no common variant of COVID that is anywhere near as mild any virus we call "common cold". In the best case (Omicron for a young, boosted individual) it's comparable with influenza in terms of severity.