i agree that it is not possible to stop people from lowering their rating intentionally. but i guess you are missing a vital point here : mmr. you can't lower your mmr below a certain point ( if your current rating reaches 1.8k, your mmr goes up from 1.6k to 1.8k if you win or lose ) therefore if we base brackets solely according to the mmr of any player participating in organized pvp, and make it a flat rating for any / all activities ( say, your rbg rating effects your 2v2 etc. ) it is a step into the right diection. while it is flawed, it is way better than current system.
what if my irl friend ( let's say he is a freshman ) wants to play with me ? while it sounds logical, do you expect your irl friends or brother to be as skilled in, say, chess ? what if you are in the national team and they want to play with you ? they can play at home while drinking a beer ofc, but not when you are participating in national league. there is skirmish mode for this purpose. you can even raise the rewards of skirmish based on your win. you can implement a completely different game mode for this purpose only. there are many possiblities.