I should also mention, there's another place it gets used - in Chrome extensions. That should use the same identity.
Google login then becomes one reasonable choice for "log into the internet". Right now it's too fractured to be a coherent identity.
That's actually good use case for the browser login feature. (when one is using some google-acc-connected extension)
But for ordinary users I don't think this solution would work flawlessly, because it is different than ones before (and users learn new things slowly).
However if that would be the actual implementation (force logging everywhere into the same acc) I agree it would be simpler for end-users. But it is not, therefore original point (browser login is confusing people) still stands. And therefore teaching users to rely on it does not seem like a good idea.
People don't need to understand oauth to use it.
(and before you pull that one again - I am supporting technically-illiterate people quite often)