Surely what you're really saying is you want an easier time to find partners.
Could just allow the queue system to filter via:
Achievements, e.g. 2k last season, 2k this expansion, 2.2, 2.4, 2.7, duelist,glad etc.
Main issue with the current LFG system is:
A) You can't do anything while you're queued. Can't join a group - thus can't do content. This is a non-issue in PvE pretty much so #doubt it'll get "fixed".
People have inflated egos and even if there are people in LFG who are of your own mmr you won't play with them because of their experience being lower. To an extent it's fully understandable, but since you're not forced to play with people of similar MMR a lot of people you could do very well with will just get ignored.
C) Rage quits and demoralization. Since you're forced to find a new team by yourself with LFG and the "rage quit" mentality of LFG the prospect of having to find multiple teams / evening, especially when you're just starting out, is going to just make a lot of people go cba and not bother.
All of them are important issues, but ( and © are the largest issues by far.
Solo Queue solves ( and ©, at least the way I described it earlier in this thread.