I see it like this.
If something becomes wildly popular, creates massive hysteria, and generates record-breaking sales, that's an accomplishment that noobody can take away from it, and it also doubles as an interesting and fun historical occurrence to note. However, it's not an accomplishment that has anything to do with how good the thing should be considered. It's indication that countless people would rate it highly, but it makes no sense for me to rate something based on how appreciated it is by others rather than by me. I feel like most people seem to adopt that view, and I agree with it.
In many ways, influence is just long term extended popularity, particularly among artists themselves. It's a measure of how well received something is, and an indication that people like it enough to copy it and build off it. Again, that is an accomplishment that nobody can take away from it, and it's also a very interesting historical milestone to note and be impressed by-- it's a fun side-note to follow. However, again, that's not an accomplishment that has anything to do with how good the thing should be considered. It similarly doesn't make alot of sense to me, for me to rate something based on how appreciated and often replicated it is by other artists. I'm using the same logic here, but I rarely see anyone who adopts this view. Influence is treated by most people like a fundamental component of how good something is.
It seems inconsistent to me to have polar opposite views on the relevance of popularity compared to the relevance of influence, because they're both driven by the same type of thing.
To me, the only thing that I'm aware of that makes influence appear to be more than just a form of long term extended popularity, is the correlation that people seem to draw between it and creative inspiration/brilliance/game-changing/pioneering boldness. Like a "where there's smoke there's fire" thing. But I feel like we should be able to agree that the fire is what's substantial, not the smoke. And in this case, the analogy doesn't work, because in this case, the smoke can come from things that aren't fire, and the fire doesn't necessariliy result in smoke. In other words, the only aspect that I can see that makes influence be seen as meaningful in terms of how good music is does not even necessarily correlate with influence. You can have either one without the other.
Case in point-- Albert Ayler's Spiritual Unity is a bold, transcendent stroke of genius that can be endlessly satisfying and has the capacity to change everything. That should be admired and be considered a component of how good the music is. He's given credit for it because that happened to result in influence, but it could have just as easily not happened depending on the circumstances/exposure. It also could have easily happened for someone else's less deserving creation. If it didn't become influential, I don't see why that would take away from the gamechanging genius of the music, even if it arbitrarily doesn't actually end up changing the game because of the whims of the listeners/artists, IMO.
Another case, I love both The Beatles and Captain Beefheart. Beefheart is no less brilliant, transcendent, and inspired, but because what he did was less appreciated and put people off, not as many artists followed his lead as what the music probably warranted. Whereas everybody was influenced by The Beatles, because everybody appreciated them. Does it make any sense that I should think they're any better because of that reason? I sure as hell don't think so.
We feel inclined to use things like that as a tiebreaker, but hell, we feel inclined to use anything as a tiebreaker-- how influential it was, how popular it was, how much the artist did for social change, how much of an unlikeable ***-hole they are, etc.
