Honest question: why doesn’t everyone just use hash functions for passwords. Generating a Base64 string from a secret salt + the website name sounds ideal. This is what I do, and it works very well.
If your password gets leaked I can just: recognise that it's base64, decode it, see your salt and then all of your other passwords are essentially open to me?
Edit: Oh, is the salt different for each site? I don't get why you'd ever do this instead of generating an entirely new password though, you aren't solving the storage problem.