Honestly, for me atleast if I had the choice it just wouldn't be worth it unless it was very cheap.
As someone who works a lot, but still wants to game as much as I used to paying a monthly service would feel like a burden if you don't get your moneys worth each month. I tend to just play Rainbow Six Siege on my PC and then only buy games when they go on sale (Humble Indie Bundle, Steam Sale, etc.) and then play games on PS4 with my girlfriend for a few games.
The idea of making competition with the traditional "console war" format would be very hard since it would either need to be another Console (Think OUYA) or it would just be a PC with a GUI for the app. With this though you lose access to console exclusives and controller specific games like Rock Band/DDR/Nintendo games pretty much in general.
Overall, it would be cool, but it could thrive better if it was for each console individually otherwise its just a downloadable version of GameFly and Blockbuster/Hollywood Video/Etc.