I've long thought Bruce Lee's comments about "no style" were overly philosophical to attempt to train from as a beginner. They are an end point - actually, a fairly common end point. Many long-term (let's say 20+ years) students of the arts I know have reached a point where, when attending a seminar, they look at each new technique, strategy, and principle they are taught and examine it for how it will work for them in regards to everything else they know. Those who do this become more dangerous to their training partners who don't, because they will find a version of a technique that fits nicely into their main art, but isn't really known there, and bring it back in.
In the end, I think Lee's concept - at it's highest level - is not that uncommon. (Some of the principles within it might be - I'd need to go back and re-read his writings to think about that, and I'm sure there's stuff that was passed along that didn't make it into the books.) Basically, as I read it, he says that techniques aren't the key, principles are the key. So, though someone may study his techniques in JKD, they shouldn't be leashed to those in the long term. I don't think it's a viable approach for beginners - they need specific techniques to learn from and grow upon until they have the understanding to bridge principles beyond techniques. That's where the technical JKD has its place.
Sometimes I think most instructors (maybe most students - I just don't know many long-term students who don't teach) eventually run into a problem. They are focusing themselves in one direction for learning, and must focus their teaching in another direction, because their students simply aren't at their level...unless they move to only teaching advanced students, where the gap isn't as large. When someone copies their thoughts at that stage - whether from writings, or by repeating their teaching methods (especially if it's how they taught to advanced classes), they may be teaching beyond the beginner's level from the start.
Back to your point (which I intended to stay on, really!). There's the other side of the aisle: long-term students of an art who work to keep an art pure. If you are trying to preserve some historical point in time (like maintaining some settler's village from the 16th century in America), then that's fine. But that's not the same IMO as continuing to practice it as a functional art. Those folks don't want to add or remove anything, which usually starts from the assumption that the art is wholly perfect, and that changing, adding, or removing will break it. That attitude assumes that some progenitor was an infallible genius, who created a perfect system. Such does not exist, IMO. If said progenitor did well, then they created a whole art that worked well for the time and circumstances in which they found themselves. That art should continue to evolve as the world around it does. That doesn't mean just anything can be brought into an art. As I said (I think) before, an art is a collection of principles, and needs some unifying bridges that let you move between parts of the art. Anything new that comes into the art must fit comfortably. So, for instance, there are strikes from Jow Ga, White Crane, and Long Fist traditions that simply don't look like good fits for NGA, so to me they are not NGA. There are strikes in Goju-ryu, Wing Chun, and Kali that do look like good fits for NGA, so to me they are NGA to anyone in NGA who knows how to use those strikes. The style is simply the set of principles and approaches that collects appropriate techniques and movements under itself.
(That's more writing than I'd planned to do. Whew!)
