Why not just buy a console then? They aren't that expensive and work OK with our garbage internet connections already.
Because consoles are in fact expensive for a lot of people. $400-500 is a lot of money for a lot of people. A subscription based model might very well be far more attractive to these people.
It is also worth noting that since Google can achieve far better hardware utilization rates than individual consumers can ever dream of (due to the virtualized nature of Stadia), they can amortize the hardware cost across far more users, those significantly lowering the cost per user, by a factor of 5-10. Whether or not they choose to pass on those savings to the user is of course a separate question.
People make arguments for this streaming all the time but all the half way decent arguments seem to boil down to "like a console, but worse".
No, it's actually "like a console, but better". You get better graphics quality, better frame rate, and roughly comparable input latency (based upon preliminary tests and claims). It will probably also perform better than 90% of PCs out there with regards to resolution and frame rate, but have somewhat worse input latency, but then console players also generally have somewhat worse input latency than PC, and they seem to get along just fine.
If Google can actually deliver on what they have shown and promised, then there really isn't any area in which Stadia should perform significantly worse than your average console game (but multiple areas where it will perform better).
Obviously people with crappy internet connections will not be satisfied with Stadia, and you can certainly make arguments about the whole owning hardware/software model versus leasing/renting hardware/software model, but then people tend to forget that we already generally rent our PC and console games and don't really own them (unless you buy them from places like GOG).