This is actually an area where I think Sony has dropped the ball; PS Now is an interesting service, and they have a pretty interesting catalog of older games from the PS2/PS3 era. But they don't advertise it well enough, and I don't think they put enough focus on new releases and keeping them available the way Microsoft does with Gamepass.
I've heard these, and they should! It would give them direct competition to GamePass Ultimate, which is a tier of service they don't currently offer (unless you buy PS+ and PS Now as separate subscriptions).
I see. But because they're maintaining datacenters for PS3/PS4 streaming I think they have the potential to go hosted, at the end of the day multiplayer servers are developer-controlled and network servers (e.g.: PSN, Xbox Live) are mostly identity services and such. (Even matchmaking isn't the network's job anymore)
[1] https://www.gamesindustry.biz/articles/2012-07-03-sony-acqui...