Yes, it would be nice to universal access to all content. But the streaming providers must negotiate licensing fees, and having a commitment to provide all content would allow the rights-holders to charge whatever they liked. That drive the cost of the streaming subscription extremely high. If it was PPV then it would work, but that is basically what you get with google/amazon's rentals.

In a different world where rightsholders didn't get to set their price, then this would be possible. That world is bittorrent ;)