NessAndSonic: I'm sure there will be problems. Possible lawsuits if games get removed from the streaming service if they try to sell them to people
That's the tricky one, they have to make it clear it is a service where games can get removed without notice, even while you are playing it. This was also the case with OnLive.
It is not really different from e.g. Netflix or Spotify removing movies/TV series/music from their service. I don't think anyone can really sue them for doing that, as long as it is made clear it is a service and you don't receive an actual license for anything you use in those services.
This also affects pricing. I personally feel a monthly fee for unlimited streamed gaming would get a better acceptance than that you pay per game. Maybe the latter will work if you get access to a new streamed AAA game for a few bucks that would otherwise cost you $60. Sort of renting, I guess Sony system has made that clear as they have different price points giving you limited access times to the game, e.g. one day or a week. That's almost the "pay per play" model, really.
The little experience I had with OnLive, from my point of view they had a problem with pricing. If you wanted a new-ish AAA game from them, the price would be the same or even higher than buying from e.g. Steam. You could argue that that is ok because you can play the OnLive version on a device that couldn't possibly run the Steam version (as long as you have fast enough internet to that device), but apparently there weren't yet enough people who found that a good alternative (to owning either a PC or a $200 gaming console that can run that same game locally).
OnLive also had some kind of monthly pay system where you had access to a bunch of games "unlimited" (as long as those games remained in the system, sometimes games might get removed from the access list and new ones added instead), but as I recall they were for the great part lower-end indie games where the argument about not needing a $2000 PC to run it doesn't work. They were not resource-hog AAA games that'd need that $2000 PC.
NessAndSonic: people hacking their game to play offline like they did with SimCity, etc.
If we are talking about fully streamed games which you play through a "terminal", then this is not an issue. You simply can't hack such streamed games.
SimCity wasn't really a streamed game, it was a locally-run game that for a reason or another demanded a constant internet connection to EA servers. Diablo 3... as far as I've understood, it is mostly a locally run game, but streams some data from the servers, so maybe it is a partially streamed game. Same for Quantum Break, apparently the video parts will be streamed, while the parts where you play you run locally. Quantum Break could possibly be hacked somehow to make an offline version where it streams those videos from a local repository. No idea how much room all those videos would take especially in 4K resolution, maybe keep only lower-quality videos offline then.