Can't subscribe to Apple TV+ while on a family share plan for only Apple Music

I have been added as a member to my daughter's family sharing plan for Apple Music. I want to subscribe to Apple TV+ as an individual, not part of the family, but it doesn't appear that I can do that. I am offered an Apple One subscription, but not just Apple TV+. I suspect it's because I'm a member of someone else's family sharing plan but I'm not sure. Why?