This absolutely won't work if it ends up like movie/TV services are now. Gamers are even less likely to sub to several different services because they have the one game they want to play that's not on the service they have. Plus games can't make money like this while Movies and TV shows make revenue via theaters and sponsors. Like strider said, paying fees on top of fees is a no go for gamers. That's why MMOs don't work on console.
Fiber optic Internet service will have to become the standard for this to be viable, which is probably a decade away from happening.
Its one of those things thats good in concept, but in reality everyone wants a piece of the pie and you'll have too many different services walling off games to under their brand. A whole new era of 3rd party wars would start that would collapse the industry because, while it worked when you paid $600 for both consoles, now you'll pay that in a few months and more on top of it if you want to keep playing all the games you want. Origin and Steam would have their own service, then Amazon, Nvidia, Uplay, Netflix would probably get into it, WB would try to make one probably.... just a bad idea all around. Sure a lot of games would be on all the services, but they would all have exclusives trying to rake in subs.