I don't think you can assume, nor is it reasonable to assume, that the initial migration of players from Unranked-Ranked was 1:1 across MMRs, which is the crux of your "average remains the same" argument.
Considering the amount of anxiety typical players have over their MMR, anyone who would subject themselves to that much stress would place a lot of importance on being good at the game, and would likely already have an above average unranked MMR. Furthermore, 1k Unranked players who calibrate into 1k Ranked, while they see their peers at 2k, 3k, and 4k, would be discouraged from playing Ranked any further, pushing the average Ranked MMR upwards.
So, really, this is a discussion about the initial sample of MMRs that determined what the "average" is, and you're arguing that it was 2k, which I find hard to believe because it doesn't really account for player psychology. If the "average" player who committed to Ranked Matchmaking had an initial MMR of 3k, then the average today would, by your argument, still remain 3k.