Well yes but at the risk of stating the obvious, the Chromecast is not a Microsoft product. I'm sure there are <insert reasons here> that Stadia doesn't currently work on the new Chromecast, but the optics of it still aren't good.
And to address the above point, I don't 'hate' Stadia, it'd be daft to hate an online game streaming service. I am however fascinated by technology, and in this instance I'm perplexed by how far short Stadia has fallen short of the promises, with the might of Google behind it.
The history is all there in this thread, I initially called 'fail' because I didn't think the world wanted another 'OnLive' (and I still don't think it will anytime soon), changed my tack when I started to understand the scope of Google's ambitions for Stadia, but now here we are at the end of 2020 and basically none of the cool shit they promised is here, it is just another OnLive, and one that Google aren't even supporting on their new Chromecast for months.
Who is Stadia for? Who wants it? Who'd recommend it to a friend or family member, and on what grounds?