It keeps the bounces at a desirable height. If the ball were just rubber, it would bounce far too high to play tennis.

It also protects the strings of the raquets and slows the air speed.
(Otherwise it would be like raquetball in an open court)

Keeps ‘em warm in the winter.

The fuzz is also what makes spin effects possible by dragging a layer of air around with the spinning ball.

physics lesson here

Because it was old Fuzzy Balls Johnson who first invented them. He was known far and wide for his fuzzy green balls and nothing warmed the cockles of his heart more than to know that women the world over in small white skirts would be fondly handling his balls.

Also the fur protects the walls and furniture when kids throw it for the dog. (Of course after a while it can get really gross and the fur is not longer a plus)

So that you can fluff up your down jacket while it’s in the dryer.

So that the inevitable jokes about balls can be retold.

To make them cuter so people wont hit them so hard.