I think there is a common misunderstanding between, “Different ways to learn” and “Different ways to hit a ball.”
These are two very different concepts and each possess different interpretations of each.
“Different ways to hit a ball” can refer to different methodologies or technical applications of physically hitting a ball. From one hand to two, from open stance to neutral to closed stances, from weak eastern forehand grips to severe western grips, there are indeed many ways to make the racquet interact with a ball. In addition, there are different spins that can be imparted on a ball which will require other ways to manipulate the racquet within a swing.
“Different ways to learn” refers to the ways in which a decidedly specific shot or stroke is conveyed by a teacher to a student. (Or, how an individual perceives the information or observes the information if self-taught.) Do we teach verbally, kinesthetically, guided discovery, or choose to let the student try to learn bits and pieces completely on their own?
Unfortunately, while there are indeed many ways to hit a tennis ball, there are only certain ways that will both biomechanically, as well as within the laws of physics, allow a player to eventually hit the ball within the bounds of truly effective means. (Being able to hit with more pace, more spin, more depth, more angles, with more touch, with more disguise, and within a greater selection of choices AND all within a concept of consistency and confidence.) There are far more ways that a student can hit a ball with inferior mechanics that they simply won’t improve past a certain point, predicated on the limitations of the chosen stroke, grip, or body position.
In teaching, the instructor who has the greatest array of cues, analogies, tools, and drills that pass on the correct hitting information that falls within what I call an “Advanced Foundation” is indeed a valuable asset and valuable instructor. Likewise, a pro who understands not only the limits of any number of particular stroke choices, but how to help the student avoid the common pitfalls associated with those patterns, (because, let’s face it, advanced stroke elements are usually seldom comfortable or familiar!), is again valuable and, in my opinion, priceless.
Sites like John Yandell’s site (TennisPlayer.net) as well as TennisOne.com (which I am affiliated with), and other on-line sites that provide visual guidance, along with valuable advice from proven instructors, provide both the idea of proper ways to hit a tennis ball as well as provide a wide range of ways in which the student can grasp those concepts.
In my opinion, we need to be clear in the difference between learning and hitting.
With these tools, the onus then is on the student to actively engage in what is being conveyed. They must recognize, emulate, practice, and adjust as they progress, in order to make the information become relevant. The percentage of value will of course be predicated on the ability of the student to take the given information and make it their own. Some it will be very minor, perhaps even detrimental for a number of reasons: They didn't interpret the information correctly, they didn't know what their own body/stroke was really doing, or they simply ignored certain aspects of the instruction. But, for others, those who are capable of correct reasoning, who can emulate correctly, who can overcome the human condition to go back to what was initially comfortable, such information is indeed priceless. No different than any instructional book.
To try and quantify through before and after videos of individuals is meaningless. Because of the aforementioned diversity in learning and interpreting, one pro's advice may very well produce an individual who was very successful. Yet, the very next student may have no clue because of a wide variety of reasons and conditions.
Thus, from my experience, (45 plus years teaching and playing highly competitive tennis, and training countless top-ranked players), I believe that most will definitely gain very valuable information from sites such as those mentioned. Is it valuable to the price paid? Well, if you got one tip that improved your volley, or your serve, or your groundstroke, or your strategy for the REST of YOUR LIFE, would you not find the money spent worth it? Of course, you have to engage the information to gain that value.