Overwatch had a feature where you could avoid players, but a top sniper was avoided by enough top players that he could never find a match. The matchmaking system could never find him a match because almost all potential matches had at least one player on each team that had him avoided. The devs eventually reworked that feature so that he could play the game. Sometimes seemingly innocuous features have weird edge cases!

Even for an average player, adding an avoid player feature would ultimately make matchmaking take longer. It necessarily reduces the number of valid matchings of players, so the system will only be slower. My guess is that average queue time is an important metric that management does not want to increase. It’s an especially tough sell because if you really wanted fresh players in your game, you could always not queue for a few minutes and you will almost certainly get all-new teammates.