In general, we don't need to ascertain that we "deserve" to do something to do it. The default in a free society is that we can do anything. What we need to deserve is the reverse: the right to prevent others from doing something. That's what needs to be justified.

This doesn't mean those parties shouldn't have the right to prevent us from streaming, I just dislike how the burden of showing so is distorted to assume one needs to justify each action one does.

In any case, the ToS explicitly says I can stream: you agree not to access Content or any reason other than your personal, non-commercial use solely as intended through and permitted by the normal functionality of the Service, and solely for Streaming.