My personal experience so far has been that every single 'Avoid Me' player carried that label for a very good reason and not because someone abused the reporting tool. Every single one of those 'Avoid Me' players would betray their own team sometimes because they think they deserve the -whatever- weapon it is they want at the moment or they just seem to enjoy betraying their team for no other reason than them enjoying such unsocial behavior.
Do you check the reputation of every player you match? Because this seems like a situation where there'd be bias towards checking people who "deserve" the label, and not bothering to check players who you think play normally.
I am not taking anything away from anyone else when I decide I don't want to play with a certain people. Nobody is forced to use such an option if it were available.
You're decreasing the potential matchmaking pool for a subset of players, so you are very definitely taking something away from someone.
Besides, I doubt you get this particular label very easily and after only a few abusing reports.
But you can't guarantee it, and even if it isn't easy to get, it's based on subjective opinions of other players, and therein lies the problem. There are a variety of false reports that may be not at all uncommon. People very easily mistake lag, or even good players, for hacking. If not that, people have vastly varying notions of what consitutes as "cheating". Then there's of course just plain rage reporting, where someone is just having a bad day and singles you out (or reports everyone they played against).
The falsely labeled players are of course only going to be a subset of players with the "Avoid Me" reputation. However, there's no point in using such a poor system in a game when you can do better, and have matchmaking be completely data driven. Instead of relying on subjective feedback from players, you can focus on specific unwanted behaviors and collect data indicative of them. Want to get rid of team killers? You can track how often a player kills their teammates. What about those run after you, spraying you with an AR if you grab a power weapon in front of them, but don't kill you? You can track damage done to teammates. Griefers who die intentionally to ruin your match? You can track suicides or abnormal KD-stats.
When a developer has the ability to track every aspect of player behavior, they can label players based on objective data about their behavior, and thus create a system that has much less room for false positive, and that is potentially much faster at catching and dealing with unwanted behavior. Not to mention, there's always a very specific clear reason like "team killing" why a player gets labeled rather than some vague notion like "cheating" or "unsporting behavior".
In other words, the reason not to use the "Avoid Me" label in matchmaking is not that it's completely useless, but that there exists a clearly superior method of dealing with unwanted behavior that could be used instead.