Honestly I hope SE waits to see how Stadia will work - as in stay around. I fully expect Google to abandon it in 1-2 years like they do most other initiatives they put in place. I'd hate for SE to devote any resources to it for Google to just say "whoops nevermind".

Also streaming games, while perhaps in the future will be the thing, right now there are not many places that have the infrastructure to actually make this kind of service reliable. Not to mention people have data-caps and such on their plans. Until ISPs want to actually invest in their network capabilities, Stadia and the like are going to be only for a very niche market in the right geographic locations.