CrimethInc's Rolling Thunder did some analysis on this a few years back. I think their conclusion was that, on one hand, anarchism's merging with a cultural phenomenon (punk, from the 70s to 90s) kept anarchist ideas alive during a period when anarchist activity wasn't especially visible or widespread. On the other hand, tying anarchist ideas to one particular culture made it of limited use to people who didn't belong to that culture, and also had a lot of negative consequences considering punk was mostly (but not entirely) a thing for white dudes.
Anarchist punk movements are definitely big in South Asia, though, and I'm not sure to what degree they differ from their North American/European counterparts. Rolling Thunder also had an article about the anarchist punk movement in Mexico, but I can't recall the gist of it offhand.
I'd say that having anarchism tie in with particular cultures could be cool and make it easier for people for people within those cultures to identify with anarchist ideas (as made obvious by lots of punks having some interaction with anarchism) - I think there have been a few "experiments" on this idea, like Graceless and Steampunk Magazine being anarchist tie-ins with goth and steampunk culture, respectively. The only obvious downside to me seems to be having anarchism tied to just one culture in particular, which also leads to the idea that that culture is an intrinsic part of anarchism.
I remember talking to some Greeks a while back and they mentioned that where they're from, there's anarchist raves, anarchist hip-hop shows, anarchist punk shows, anarchist whatever - it's not tied to one particular scene or subculture. And I think that's awesome. I don't even really like punk music anymore and almost every anarchist social event I see is a punk or metal show. Eesh.