The reason must have to do with either judging or playing the game (otherwise, why bother?). I'm no physicist or aeronautics engineer but I presume the fuzz is relatively negligible on ball speed over short distances, so it's probably not related to how the ball flies. It also doesn't seem realistic that it interacts with the racket or the court. One not so serious thought is perhaps it's got to do with net dynamics but that seems like an edge case I professional play. I haven't really watched tennis but I imagine most volleys end in balls bouncing out of bounds or a player not being able to return a hit. A little excessive to add fuzz for that. I also considered that maybe it's a means of having something adhere to the ball (like if it bounces on the line) but they have high speed cameras and line judges for those sorts of things. Guessing it's not that.

If it doesn't affect the dynamics of the ball or the adjucation of a play, it seems to me that it's instead a more general indicator. You touch the fuzzy ball before every serve and feel the fuzziness. You have a finger sense for a good ball and worn one. If the ball is fuzzy enough, it's good enough. Therefore, it seems to me it's a quality indicator for players to know when to switch out.

And I looked it up, it turns out I'm quite bad at physics! Won't spoil it any further for others trying to guess.