While I'd love to say that the biggest problem is being able to join matches at a high MMR, it's not. That graph proves it.
There are so many people in the <2000 MMR range that the issues that affect the highest players (in regards to matchmaking itself, not game balance) are unfortunately quite shallow.
1. As far as I see it one of the major problems is starting players at 1250 MMR. 1250 is exceptionally low, and while it appears that the peak of that curve rests at about 1400, I'd be willing to bet that a fair amount of those players at 1400 MMR are relatively new. MMR is only calculated against other players. This means a new player who happens to be ok at the game can really stomp at that initial level, and his or her MMR won't be raised too significantly, thus forcing him to continue playing the game at very low levels for some time.
My recommendation is not original, but I'm not sure who initially posed the solution. Give players a single question survey the first time they sign on.
"How experienced are you with arena style shooters?"
a) lol wut's a computer = 1250 MMR.
b) I've played call of duty once or twice = 1500 MMR
c) I've played Unreal Tournament for years = 1750 MMR
d) I'm a smurf = 2000 MMR.
Obviously reword the answers, and the last one is for more than smurfs, it's for people that are just very very good at competitive shooters and want a challenge. This will help get people acquainted with their appropriate playstyles faster than the current system, bring people into the higher MMR range faster and should hopefully do a bit to alleviate both boredom and frustration on the part of newer players.
10. The way in which matches work. Autobalance actually does a pretty decent job if a few conditions are met. Those conditions are: relative MMRs are accurate (see solution number 1), the game does not add more players mid game, the number of people on each team is even, people don't leave mid match.
Now, I'd love to see casual and competitive servers implemented, but as a non-data scrounging high MMR player, I'm actually not sure whether or not that would be ideal in terms of the playerbase. But, if possible, maintain casual servers in which people can join mid game, leaving doesn't really matter, MMR isn't affected (or is only minimally so), and MMR isn't restricted.
Then, implement competitive servers, where the game can start with a minimum of three players per team, offering a start vote to start to the server at 6 players, 8 players, and 10 players, while at 12, it just starts. These are MMR restricted to a degree, but post 2200, as Xacius suggested, you've sort of entered the wild and can be matched with whomever is looking at that time.
Leaving a competitive server results in a time out from competitive play, playing in competitive servers nets an HC boost of some sort, and MMR is directly impacted. For the sake of minimizing the impact of smurfing in competitive play, it is restricted to an arbitrary level and above. Ten? Fifteen? Don't want to go too high, but in combination with the initial suggestion, hopefully alt accounts will reach an appropriate MMR by the time they hit this level.
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The first problem has a relatively simple fix, I think. The second, not so much, but hopefully some combination of the two will aid in new player retention and grow the playerbase.