I worked on a browser extension similar to what you are proposing for a tech company. There's also a project out of Stanford called PwdHash. Such schemes are nice, because they do increase the entropy of the generated password and make dictionary attacks more difficult.
The main problem I ran into were pragmatic ones. The solution works 99% of the time, then you run into a web site that only works in IE (and your extension only supports Chrome, Firefox,and Safari), or you run into a phone support line that requires your password, so you can't use the client side implementation.
As discussed above, it's also not perfectly secure, since it still subject to dictionary attacks unless the large secret is stored on the client, which is usually not desirable, because client side storage of the auth credential is unreliable in browsers and ties the user to a single computer. Also, a system that relies on client-side stored secrets might as well not use passwords at all.
There's a standard called Secure Remote Password, which attempts to take this a step further. It's based on knowledge proofs, rather than exchanging a cleartext hash. As such, it can't be dictionary attacked by an observer, unless the observer colludes with the authenticator.
In comparison, PBKDF2 is not particularly secure. It's effective just a slow hash, so constructing the dictionary takes longer.