To be honest there was project for that first off it was ONlive then PS bought it and do it as PS Now service. But the problem with streaming games is not about device power but the time, internet speed ect.
You can watch on netflix movies and there is no problem with that, but when you play games, especially fast action ones there is a BIG problem about command responsiveness - In easy way;
When you press button is TOO mach to waiting to see action to response to your action. So it's happen that you wait even one second! to see response if you are to far away from serer and even if you had a server in your house there still we a problem with internet and sending and receiving data.
If you will play online game like CS:GO it can go worse because you need fast reaction and precision.
That's why right know your technology and even PS5 dosn't have solution to problem off that.
Oh yeah latency would kill the online games. I wonder if they are working on a cloud service now that can handle it for the average household.
I use steam link to play games on my couch tv, But i have cable lan to conect steamlink and my pc. so yes to stream games over the internet its very usefull have a good speed