Sounds great on paper but I'm skeptical.
Not only you will need a really good internet connection and wifi, but also being close to a Stadia data center. The best possible case scenario will probably be a latency of around 50 ms, but I'm guessing the average will be closer to 100 ms which is too much for many types of games (specially competitive games the streamers play).
Heck, even streaming in your local network isn't such a great experience these days.
I love the idea, but realistically we are still very far away from streaming games replacing consoles or PCs. Many companies have tried (Nvidia, Sony, etc) but no one has succeeded for the simple reason that latency is not there yet.