Could it work?
It would need every playable game's publisher to sign onto it, so no, probably not. It wouldn't have every game.
That's way too cheap. More like $30 a month
They'd have to get the publishers in on it, and I imagine the breakdown of monetary distribution would leave a lot of them unsatisfied. At least with the current system, they get 70-80% of each sale. With a flat monthly rate, who's to say that everyone gets a fair share?
Not only that, but very few Steam users would adopt it, given that people mostly just play 1-3 games constantly on rotation.