Apparently, it wasn't all that uncommon to not be able to read or write music and to have a scribe pen it down for you.
https://www.straightdope.com/21343780/if-irving-berlin-could...
https://www.straightdope.com/21343780/if-irving-berlin-could...
Doesn't read | write sheet music (see youtube interview linked in GP comment)
Oxford English Dictionary:
musician - A professional performer of music, esp. of instrumental music.
Wikipedia:
Timothy David Minchin is a British-born Australian comedian, actor, writer, musician, poet, composer, and songwriter.
Also - pretty much the entirety of Indonesian traditional ensemble musicians (Gamelan and other) going back to the bronze age - no sheet music so no reading writing music - they train like Homer delivered poetry and use non Western scales - their music is available in notation, but notation created by westerners.
Here's a bit about Western students learning to learn music w/out using sheet music ...
https://www.youtube.com/watch?v=xHgdrzgtBik
They're not some minor outlier either, btw - "With over 278 million people, Indonesia is the world's fourth-most populous country".