I think the answer's obvious -- replace Facebook with an entity, hypothetical at present, that's controlled by its users, not a corporate board of directors whose loyalty is to themselves and to stockholders, people for whom subscribers are a product being offered up for sale.
I'm obviously speaking hypothetically -- there's essentially zero chance for such a thing, given the modern Internet and the current political environment.
> If I can legally take a photo, should I not have the right to have a company analyze that photo on my behalf?
The unasked question is whether the analysis is carried out on your behalf.