One point I'll add here that I should have included: there are different levels of being "self-taught" that can make a difference.
A 'self-taught' player who studies the game, observes what top players do, why they do it, and understands how they do it...then emulates these patterns is going to do far better generally than a player who goes out and tries to figure out how to hit the ball over the net with no preconceived way to accomplish this.
Kid especially will learn the latter method...parents can be the worst person in this because many simply toss balls to a youngster and tells them to "aim higher" "swing slower" "swing sooner" etc...hoping that the kid will eventually learn to aim, swing, and time the shot...which they will. Unfortunately, there are dozens of ways to ineffectively hit a ball over the net towards some given target or zone. By replicating this ineffective method of hitting the ball, the parent (or coach) will effectively limit the potential of the kid.
Adults, even skilled athletes, I've seen learn this way too. They develop an ability to make the ball go over the net quickly, but they stagnate soon after and fail to really make any strides later in life, unless they fight through the frustration of changing the dynamics of their ineffective stroke.
I've seen dozens of players with very few lessons excel. Why? Because they took on the role of "coach" themselves by studying the game as I've described above. They create their own "lessons" by watching, carefully observing, asking questions, and coming to correct conclusions.
Yet, even these players can benefit from lessons from quality instructors. It can save time, clairfy uncertainty, and avoid some mistakes.
I am not advocating everyone SHOULD take lessons. I'm saying that it can help players develop the proper strokes that can help them reach their potential and avoid working on ineffective strokes that can hinder this goal. But, players, especially in today's world of Internet, can study the game better than any time prior and get "lessons" throught this technology.
However, nothing is better than having a great coach who knows his or her stuff, and the personality that can connect with an individual.
Dave Smith: Author, Tennis Mastery/Coaching Mastery;
Senior Editor, TennisOne; Dunlop Master Professional