We're not talking about OnLive. Just a subscription model. You'd still download and run the game on a local client. As for the entire "servers" argument, that is true of Steam already. If they go poof tomorrow your entire Steam library is gone with them. This is why only big platforms like what EA is going with Origin can realistically do this. Discord is also doing this now with Nitro.
Onlive was a MINOR point about how a subscription based model could, at least theoretically, work. And Steam is a poor example, because they're not making subscription dollars from consumers, but shaving money off the top from developers, that's a WHOLE different thing. It's technically still driven by consumer sales, yes, but still not subscription based, and it's library is massive, and certainly not a single game. So, even if Steam WERE subscription based, which it ISN'T, it wouldn't be an example for this topic.
Edit - It occurred to me you may be making the point that non-multinational companies could use a steam-like service to get around server costs. In theory, this could be true, in practice, it's hard to say. Valve would have to okay such measures first, it remains to be seen if they'd willingly do so while others like Epic Games Store and GoG could take away any business they lose if this generates ill will. Valve's previous missteps with Steam are arguably why Epic Games Store has consumers and GoG has remained afloat as is.
This would also only solve for the PC market in the first place, in the console market it just isn't happening any time soon, see XBONE and PS4 competing launch announcements for why.
Basically what I'm saying it isn't as simple as "we can get consumers to pay more, therefor it's more lucrative", and that other markets use it with success is not a measure of whether the game market can or not. Those other markets lent themselves to it more naturally, there's always a reason why they DID and games DIDN'T.
Again, I can see a Netflix for games or episodic model dominating, but a scheduled fee for games is only ever going to happen with MMOs. That's not to say companies can't or won't try it elsewhere, but there are too many reasons beyond just consumer backlash why it can't and won't work out for them.