So there exists a browser extension to implement what you desire, it is called HashPass.
However, if you use such a strategy, you *still* must have a password resilient to dictionary attacks. The attack scenario it provides *some* protection against is if you use a site that has poor security storage policies, without your knowledge (e.g. stored in clear text). The idea is that if such a crappy site gets compromised, it's view of plain text password is the end result of your client side salt, which now can be run against a dictionary attack. It basically is ensuring that *someone* is doing a secure hashing strategy that would reasonably protect a strong password in the manner the server side *should* be doing anyway.
If an otherwise secure site adds what you describe, it would do nothing to enhance security. If your password is *truly* strong and they employ proper salting and one way hash strategy (scrypt, PBKDF with adequate passes, what have you), then a leak of their password database is not actually that big a risk. If your password is weak, then the salting strategy client side doesn't add anything, as they could modify their brute force attack to do the client transform in a trivial fashion, and they can work their way back to the password you *really* use.