I'm not a native English speaker, so forgive my ignorance, but isn't "women" a noun, not an adjective? Why not just say "female artists" or "female writers"?

The English language is unusual in that it doesn't have gendered nouns, so we find other, often quite clumsy, ways to indicate it. You're right that it doesn't make sense grammatically; we say it that way simply because it scans better.

As a side note, I've also literally never seen anyone say "men artists" or "men writers". What gives?

Patriarchy. Society defaults to the male. That's not unique to the English-speaking world, of course.