Google bought YouTube when it already dominated the video sharing market. Stadia might not dominate the gaming market in a couple years. Google likes to kill products that don't consume all, at least, that's what it looks like to me.
Stadia strikes me as an end-run around the competition of Twitch game streaming. One way to beat the competition is to reduce the friction around your own offering. The big draw of Stadia is the reduced friction between streaming and gaming.