Yes, being able to write is a good thing.

You can get so far with just an aural tradition but the invention of writing helps.

It's way more than that. They are just more fluent at creating things like melodies and harmonies that "work" without essentially starting from scratch on every composition.

I know music notation and can write things down, but I'm not a good composer. I'm at the mercy of others to write new material if that's what I'm interested in playing.

And writing it down in a way that other musicians can understand is of nontrivial value if you want people to play your stuff.