I got a similar idea when I saw this link. But I think it would be better to have it as a browser extension that automatically hashes the password/passphrase for you, depending upon the site. Different salt for different website, that changes on the click of a button(to deal with enforced password expiration, or password changes), and maybe a different hashing algorithm for different levels of sites.
The idea is to have one password, with a salt(or service name) for all services. To make it a little more secure, you could set up different levels - email and social, news sites, games..., basically any way you want to do it, and have a different passphrase for each level.
When changing passwords, you just need to change the salt of that particular service.