Unfortunately that would cost you about the same as a cable subscription due to the licensing costs.
Lots of content = its all worth a whole lot less to people.
Notice how cord cutting has accelerated as people realize a) cable is far more expensive than the value they get out of it and b) the experience with Netflix, Amazon, etc has improved and new players have arrived (MLB, HBO Go).
When people go out of their way to download or stream a show, it's not usually background. Providers know that, that's why they insist on shoving 20 minutes of commercials in front of you for a 40 minute show. You're captive.
I truly believe there are a lot of people out there like me, who are willing to pay existing cable prices for completely on-demand content. They just don't know it/think about it because they aren't navel-gazers like we are.
Netflix already seams cheap at $8/month, especially with their laissez-faire approach to families sharing accounts.