Sure, you don't have to fit them in a category if you don't want to. I mean it's no biggie. For some it just makes it easier because as you stated it's how the brain works and a lot of people do it automatically.When I'm organizing my shop, everything belongs in a section/category that makes sense. All painting and drywall stuff in one area, all metal working in an area, all plumbing, electrical, wood working, etc. All fasteners and hardware are separated and organized by type/use.
Same with my kitchen cabinets, drawers and the fridge. Things are organized and separated by type/use.
When it comes to music, this system doesn't work for me. I can't remember ever listening to music and needing to know what category it fit into.
If someone asked me what "kind" of music pink Floyd was, I'd say,...."um,...pink Floyd".
I like Tool. What "kind" of music is Tool? Don't care. It's Tool. That's what kind. I like DMB. What kind of music is that? Don't know, don't care. I like steely Dan, Jethro Tull, SRV, Stevie wonder, Ohio players, rush, yes, etc etc etc. It's all over the spectrum.
I don't need to fit any of them into a category. It's not a kitchen or a workshop. It's music.
I get how the brain works and the obsessive need to compartmentalize everything. I just can't relate to why so many people do it with music.
If someone asks me what thrash metal is there's a bunch of bands that immediately come to mind and I'll name them; Anthrax, Forbidden, Exodus, Slayer, Testament, etc.
Same with prog rock. Without thinking too much about it it's the usual names like Rush, Yes, Dream Theater, Fates Warning, etc. For me anyway. Someone else may name different bands and that's ok too.
It's not something that I personally think about for hours every day nor is it a subject that's taken too seriously. it's not a matter of life and death.