I'd direct you to a review of Onlive, a previous startup doing exactly what you say[1]. The take away is exactly what I've heard about Stadia:
"OnLive's streaming game system is a really cool concept, and the ability to access a library of games with no downloads, discs or storage worries is definitely cause for excitement. Some gamers will be put off by the occasional lag, though, and the list of currently available games isn't hugely tempting.
Still, OnLive is an exciting proposition, and it costs nothing to try it out. It probably won't suit you if you're pernickety about lag and image quality, but we'd recommend checking it out nevertheless."
I personally think that, after seven years, Google seems to be in the same place as a much smaller company, speaks to why it feels disappointing to me.