Why would the styles by "natural".
Because they are found by the movements of the population without a coordinated guiding hand. Even with the 800-lb gorilla of D&D in the room, we find that players have a wide variety of likes and desires in their gaming, and generally have the freedom to experiment and move to what they actually want. Gamers still gravitate to what they like not because they are told, but
because they like it.
In any event, I don't think statistical methods are widely used to identify styles and movements in other aesthetic domains (music, visual arts, fashion, etc).
Boy Bands. Even the most basic of methods yielding wildly popular (and financially lucrative) work by finding out what people wanted, rather than what critique said was good.
So I'm not sure that they would be very useful in RPGing either. Of course marketers would use them, but marketing is a different domain of inquiry from criticism.
Criticism is largely divorced from the broad public's experience of creative works. As such, its ability to help us create things that communicate broadly is limited. If you want creative works that is highly valued by a small number of like-minded people, following criticism is a good way to do that.
Following theoretical frameworks divorced from actual experience does promote creativity in some, and it'll produce a random walk that will eventually uncover something new that's useful to the broad audience. This is, in essence, what happened with the Forge and the Big Model - a goodly bit of creativity, and some cool new stuff was created. This was an inspiration to many, but once the inspiration played out, the models fell by the wayside, because they didn't tell us anything real.
If, however, you are interested in creating works that do something good
for the audience, knowing what the audience actually does is terribly useful. This is what WotC got out of their own segment analysis in 1999, and again as they took significant input from staggering numbers of playtesters in designing 5e.
So, by all means, engage in criticism. There's value to be found there. But that does not decrease the value of finding out how people actually play.