My point is that just like I decide if I am going to distribute to streaming services, I also should be able to decide if I am going to allow models to train on my work. Isn't this something obvious?
It is not just not obvious to me, but goes entirely against my mental model.
Staying with your example of music or book authors - a musician or author might choose which distribution platforms they work with, but they don't have the ability to tell a particular shop to not resell their record/book, let alone to tell a particular "consumer" not to listen to it / read it.
Yes, I agree with you and when you give distribution rights to a third party they have the distribution control. How I imagine this mess being resolved is by a middleman, like the distribution services in music, there need to be companies licensing training data, from which artists could take a small cut.