I personally don't think it will lose any players this way. I think, if they fix the matchmaking and make it so people with the same skill level will be in the same server. It will be beter for new players to join as well for other older players to play against people with the same skills and give them a way to improve.
I started testing something with a complete new account. Bronze server T rank. What I noticed is that people who I matched up with didn't want to play with a T and either teamkilled to get kicked or just leave when there is no enemy yet. Then when there are enemies. I get queued agains max rank gold players or just very high ranks in general. While I get ranked with a other T or a beginner player. As a new player my impression would be to never play this game again, just the way you get treated as a T.
So how to lose players? Well the way it is now. You will definitely lose players.
Yes. I know this way is not the only thing it would fix and there is also a ps. That said: Or make it that Bronze can only join bronze and up, Silver can only join Silver district and up etc. So there is not one option. And with a little matchmaking fix & maybe rework with the treaths at the moment. The game will be more playable.