No, you're right. We have password managers built into browsers. That just doesn't work the way we'd like it to. Because of this we have the extra kludge of requiring extensions like LassPass to keep passwords safe and sync'd between browsers/devices. We know that isn't an optimal solution (but it does work...)
Instead, what we really need is some kind of identity management built into the browser. We already have something similar to this in terms of private client certificates. You could setup your browser to authenticate you to supporting websites via a client certificate. The problem is, no one is going to do that... it just isn't practical from a workflow perspective.
Instead, what I'd like to see is some kind of portable identity solution (similar to a certificate) where you could authenticate with your browser, then pass off public keys to websites. When you'd like to login, then the website queries the browser, and the browser either authenticates you by signing a message back to the server (with your private key). It could be quick and easy... hell, the major OS's now have KeyStores specifically available for just such a use-case. It just needs a spec for browsers and servers to be able to implement... if only.
It could also be a federated system setup outside of the browser, but those are also hard to get people to use (although Mozilla has done a good job in trying). My last two jobs (research universities) both had single-sign on options for web applications to use. It was wonderful. Now we just need something that the browser itself can manage.
This is a real chicken vs the egg problem, but if we could get a system like this, where we don't need passwords, life would be so much easier.
Maybe someone needs to re-invent Kerberos, or at least re-brand it :)