Imagine a 1v1 game (like chess), four players of equal skill, and initial MMR values of 3.
Everyone in this example has the same underlying skill, therefore everyone should have similar MMR values. The ideal MMR histogram would essentially be a single column at 3 (with some oscillations).
ideal MMR histogram of 4 players of equal skill
With Elo or Glicko, this is indeed what happens as long as matchmaking is random. However, once skill-based matchmaking (SBMM) is added to the mix, it all goes to shit.
MMR histogram of 4 players of equal skill with perfect SBMM
ASCII Example
With perfect SBMM, the MMR distribution will become uniform over time — exactly the opposite of what it should be. The “correct” MMR distribution in this case should be perfectly tall and narrow (constant), but SBMM leads to perfectly short and wide (uniform).
This scenario is simple enough that we can step through it by hand: