Yes, I am aware that this is the case. But this is a problem with the business itself, not game streaming as a medium. If we return to my original post, you can see that I am talking about how I wouldn't be averse to streaming some games if it functioned like a rental service -- I'm not saying that that is how Google/Microsoft Streaming Service or any other such platform is going to work.
The most likely model would be that you pay per hour for the thing you're actually consuming: which is the CPU time on the high-end gaming rig. The better way to conceptualize this is to compare it to appliance rental services, the type that will rent you a fridge, TV, VCR etc. The content isn't what they're selling. This as I said replaces hardware costs. The costs of actual digital licenses are so low however, that you'll just pay per hour and have a library of choices. If they time-limit any particular game, then you might be excluded from playing what you want when you want, and thus they
lose money, so they won't actually do that.
The way it'll work is that you might have to pay for a license for any specific game, but once it's in your library, it'll be there forever. but you pay the hourly rate for hosting whatever you play on the service. They might have some cross-deal to cover licensing: such as, if you own a game on Steam, you have the right to stream it from the third company all you want, and they use your steam ownership as a sort of legal cover.
Sure, you are limited because you're paying per hour of play, but it's not actual a "rental" of the content. That would be like saying that because AOL used to charge per hour, they were renting websites to you.