I have never using OnLive, did they support playing via browser? Browser solution is key to this as almost every device support modern browsers capable of ruining OP solution.
It's certainly not the key to getting a game on every device. I can't think of one browser game that people play on their devices. Even Words with Friends, the simplest 2D game you could think of, is not used from a browser - most people run the native app for that.
Because of performance, but streaming games solve this problem. Full screen browser wouldn't be any different than native game client.