In modern gaming responsiveness is the prerequisite to everything. You can't fight the laws of physics. Server-side only latency hiding just does not work: there is always a noticeable delay between a key press and visual response.
In addition a decent gaming PC doesn't cost much these days and games on mobile devices are as enjoyable as desktop and console ones. They will get even cheaper and cooler with time.
There is no reason for existence of such a service.
It is not available in my country, so no. Actually after your comment I've read and watched several modern reviews of the service. Players don't seem to be complaining about the latency so maybe it is really not that noticeable as I thought it would be. Thus my initial point about the latency does not hold much water.
I never much cared for UT3 on the service (maybe it was the game, maybe it was the connection, but it felt sloppy) but Red Faction 3 was fantastic. That's a physics-based third person shooter/action title. I beat the whole game on OnLive.
In addition a decent gaming PC doesn't cost much these days and games on mobile devices are as enjoyable as desktop and console ones. They will get even cheaper and cooler with time.
There is no reason for existence of such a service.