Regardless of theory, I know from personal experience that I learn physical skills much better if it is taught in several different specific ways - e.g., demonstration, simultaneous with word description, as well as an explanation of why it works. Receiving verbal feedback and analysis on what to correct is also very important to me. Without any one of these steps, I learn physical skills poorly. I've known other adults with similar experiences.
OTOH, I've met people who say they often learn best just by watching - including many of the best athletes, especially good performance dancers. (In part, I think, because they are strongly selected for an ability to learn in such a fashion.) Others feel a strong need to be physically guided through the motion. Likewise, I tend to learn academic skills analytically, from concise, well organized textbooks. Pure memorization works very poorly for me. So do long drawn out lectures, videos, and (from my perspective) overly interactive web pages.
I've tutored math to kids and adults, and taught low level skating and low kayak classes, and I can tell you for certain that the optimal learning styles of many of these students was much different from that of many of the other students. For example, many young kids learn can not learn physical skills if you use too many words. I've also found that many of the kids and adults who are described as learning disabled, or are having trouble in school, can be taught quite well, and are actually quite bright, if you analyze the ways they learn best, and adapt to them.
I believe a remarkably large fraction of the math students I've tutored, learned badly solely because they got bored. Most modern textbooks, lectures, videos, and collections of web pages, are too long and repetitive for them. I often summarize 10 or 20 pages of text, or an hour or two of video, down to 1 or 2 pages, and find that helps most of these students a tremendous extent. (Unfortunately, that involves a lot of preparation time by me.)
The differences are so obvious, if you try to teach individuals, that I think the only people who would claim that such adaptation doesn't help, are people who are unable to adapt.
However, adaptation is much easier to do in a private teaching or tutoring situation than in the large group classes that many sports and academic teachers are stuck with. I think that if you teach a group the same skills over and over using all their best learning styles, they will probably all get bored, and most would learn poorly. Perhaps that is a reason for the multiple learning styles controversy - that it isn't practical to adapt to all the students in a group setting?
That said, I admit that the two most apparently effective AND popular teachers I've taken group lessons from, one who taught physics, one who taught kayaking, both used very similar teaching styles: very concise, extremely well-organized lessons. They started with and demanded full mastery of the fundamentals, but progressed to elements that challenged everyone. I wish I had found a group skating instructor who did the same. But I assume there were other students who had trouble with those group lessons.