You can buy games and just play them, 1080p60 on hardware you never have to pay for.
Or pay Pro and get 4K, HDR, 5.1 surround sound. Which actually works great.
Stadia has a ton of hate from the gaming community it seems though, articles came out the first few months bashing it but I've had at worst visual hiccups on a wireless mesh network...
Honestly, this worries me the most. There doesn’t seem to be a way to transfer the licenses out of stadia, which means, even though you “bought the game“, you’re still at googles mercy for your continued enjoyment of the game. What if they decide that the hardware costs are too much for Google, and you now have to pay a monthly fee? What if they decide that stadia is not the success they hoped for and close it down (which Google is not known for doing at all…). Unless there are clear migrations paths away from stadia, I’d stay away from it because Google have shown that they are not afraid to change/EOL any of their products with no regards to their existing customers (just look at their lifetime free photos service, etc)
Now, why do I buy games on Stadia if I agree with your point about not owning the game? Well, portability is sometimes nice. I can throw a Chromecast in my bag and play a game anywhere. It's a supplement to how I game, but I don't think it will ever be the primary way.