I don't think Stadia will catch on as easily as you think. Its a new service so people will be naturally wary, it's a Google product so people will be aware it could be cancelled at any time and to get the most out of it, you still need to have a really consistent internet connection. These are major red flags for me at least.
That's assuming that the quality of the service is on par with traditional platforms though. Latency is a serious issue that will be a deal breaker for competitive players especially if it's not top-notch. Especially for something like fighting games where the FPS is so critical. They also said that Destiny 2 won't have cross-play with PC so if this is a sign that this service will be missing basic features than it gives people more of an incentive to stick with current options whether it's a console or PC.
We can't say for sure but I bet Stadia will be released half-baked and it'll do a lot of damage to the reputation of streaming technology. Google is being pretty ambitious here and I just don't have confidence that the product or consumer interest will be on point.