Everything (pretty much) that TM posted above is correct. However, it is only a piece of the whole picture. The piece he sees as a professional instructor. Sort of like: if all you have is a hammer, life is a series of nails (even when it is a bolt). My point being that everyone learns most efficiently in different ways. In my experience many women for example learn best by the nurturing approach of a tennis instructor, sort of the "full meal deal": verbal, demonstration, critiquing, hands on guidance, video... all of it.
It is also common, in my experience that there is a substantial minority of men who learn best by visual emulation. One can argue whether this would be beneficial since an individual could emulate the "wrong moves" but that is a chance everyone takes since all of us know there are poor instructors at every level, just as there are poor or inefficient moves that could be emulated then grooved. However, there are also more and better websites, for example that have very high quality demos from multiple angles in extreme slo-mo of strokes that are worth emulating.
As an aside using the "even Pros like Tiger Woods use a coach" is a bit disingenuous since TW is working at his profession where it is worth it to him to spend $500,000 to improve his game 2%, since that 2% might net him $10 million. It may not be worth it for many club players to spend $2000 to improve their game 8%, not a rule but just a different perspective.
Lastly, there is a myth that there is a magical perfect stroke mechanic that if adopted will transform your game to the next level, a level you could never reach with your previous stroke mechanics. I am not responding to the Strawman Argument that uses completely disastrous strokes of a rank beginner to make their case, rather the common stroke mechanics seen on courts all over the world of decent players. This topic is quite deep, perhaps too deep for a single post on this thread, but read: The Lure of the Big Game by Vince Ng, it covers this topic in great detail.
Lucky makes some very valid comments here, many of which I agree with to a certain degree.
We will never be able to know that a player who uses more prolific strokes would end up being a better player than if that same player used what ever came natural.
However, it can't be argued that skilled players, those who have indeed progressed past those which could be considered mediocre, average or unconventional, do not resemble those players who use such ineffective shots. Thus, it would be safe to say that if you don't resemble skilled players, you probably won't become one. And, if you can't emulate such skilled players on your own, you will need some help.
And while your Tiger Woods scenario is probably quite accurate, it doesn't negate the issue that even the pros use instructors to improve...regardless of cost or value. My point is that they still use coaches.
And while there are indeed "poor" coaches out there, it doesn't take a lot of work to determine if one you are considering is a good one. Look at who they have coached, watch them teach, talk to people.
But, would you not take your broken car to a repair person? There are poor or dishonest repair people in this world...should I never seek repair because of this concept?
I don't propose that all players adopt the exact game of a Roddick or a Sharapova...however, there are fundamentals that exist among all skilled players pros or solid juniors, skilled club players or seniors, and the like, that all players should strive to include. This can be helped along by someone who knows how to teach, and someone willing to listen and get past some of the discomfort that such strokes tend to feel like when first introduced.
The reality is, skilled strokes are seldom comfortable for beginners. Thus, if a beginner is going to try and play tennis, why would they use form that feels uncomfortable? Unless they are able to understand what they are striving to accomplish, they will continue to use use ineffective form for ever. That is a fact.
And, yes, while I'm a teaching pro, I would never try and let my 9 year old daughter try to learn the piano by herself. (Even as there are some really bad piano instructors out there, I'm sure!), nor would I expect her to learn to play tennis well by herself, or Karate, dance, gymnastics, violin, and musical theater. (All of which she is doing or has done in the past.)
Thus, I respectfull submit this question to anyone: are you willing to bet that you can figure out all the nuances, strategies, footwork patterns, balance issues, spins, and shot choices on your own? Or, would it be perhaps a good investment of your time and money to have someone who has provided others with such skills provide you with the guidence so you don't make the same mistakes that millions of players who can't get any better have done?
If a person is so confident that they can achieve such skills (if, indeed, that is what their goal is), and they are willing to study and research such methods and video tape themselves to be sure that they are doing the very things they THINK they are doing, then all the power to them.
I teach at a large facility and you can always see the players who either think they can get better on their own or they simply don't care...but, either way, my students almost without exception, end up passing those players by. And, most of my students, (even my 9 year old!) can look at such players and point out where their limitations are.
The bottom line is this: Skilled tennis is the act of hitting more effective shots more consistently. It is also the act of defending more effective shots more effectively and consistently. Many of the techniques that players devise on their own fall short in both of these areas: They either can't hit more effective shots, (hit with more angle, spin, disguise, depth, pace, or touch), or they can't keep the ball in play short of dinking, bunting, blocking or simply praying! that they will get the ball back.
Everyone has this choice, certainly. I never get upset when players choose to learn on their own. However, somewhere down the line, many of these players are the ones who get upset because they can't get better.
Yet, such players, when they finally admit they didn't learn very well, eventually come to me for help. But, unfortunately, because they are so ingrained in their stroke patterns (and revert to them in competition), they have extreme difficulty in making significant changes.
This is the person I feel most sorry for: They so much want to get better; they see others who are better and wonder why they can't play like them. Yet, among the 3000 + players I've taught, very very few have such remorse or feel like their lessons were a waste of money or time.
I write this not because it will benefit me, (I doubt too many of the members of this forum will be flying out to specifically take lessons from me--although some do!), I write this to help players make a better, educated decision on whether lessons are right for them.
I'm also not here to argue...since, I gain nothing from winning or losing such an argument. I do write here to give back to the game that has given me so much. And, if people are coming to this forum, they probably do indeed have a vested interest in themselves reaching their potential in tennis.
Never have I seen players reach their full potential in tennis, or any skilled activity, without some legitimate help. However, I see thousands of players who have all the skills needed to become skilled, but because of the way the learned or the way they were taught, fall far short in reaching their true potential.