Am I crazy in thinking that this whole problem should have been solved a long time ago by making password management a responsibility of the browser, either by baking it in or mediating the exchange?

Combined with a simple standard for credential exchange (get request to example.com/login to get the list of required fields, post to https://example.com/login to login. Or more likely, some existing standard that handles more cases and is already thought out) this whole annoying problem is no longer affecting every person who uses the web.

Is it too late for this? I feel that it probably would be very difficult to make this work now, it's too late and the browsers wouldn't go up against google and facebook who now want to own and track your identity.

That makes me sad, that kind of stagnation cuts off whole important areas of progress for web users.