If I ran a popular consumer facing service, I would definitely
not be inclined to provide a developer API. That's a risky business proposition. And as a startup I wouldn't hitch my business to a developer API on such a service, which is an even riskier business proposition.
That said, I'd love it if Netflix or Pornhub provided their VOD infrastructure as a service. There's a lot of space for content platforms that don't compete with them directly, but are infeasible to get off the ground.
I think a better question then isn't, "which services should have APIs?" but "which companies should provide IaaS?"