So ... music streaming is $10 a month, which would be $120 for a year.
Prime is $119 per year.
Exactly - if someone just wants access to the free tier of Prime music, they might as well just get Prime. If you want full access to Amazon Music Unlimited, though, that's additional money even if you have Prime. It's another $8 a month, or $79 a year if paid annually.
I have Prime and also use AMZ music unlimited with the annual fee. I didn’t find that much music I like with just the regular free offering, but with AMZ music unlimited, I'm finding about 90% of what I look for. I think there are now something like 50 million tracks available on AMZ music unlimited. I'm happy with this arrangement for myself. I find the Prime membership pays for itself, especially since I also use the Prime Visa card. That requires Prime membership to get, and offers 5% back (via points which you can cash in) on most AMZ purchases and at Whole Foods. (Sorry If I sound like an advertisement there!)