I've seen a few people start developing this general kind of password system for their personal use, but they usually end up giving up after running into a few problems that make them realize that there are some annoying issues involved. That's what happened when I started doing one a few years ago, when I was trying to make something a bit more convenient than the classic encrypted text file full of passwords that I was using.
I took a similar approach, using a master password, something that should be per site (domain name), and a password version number as input to a key derivation function to get the password for the site.
That's where the first problem showed up. Where should I store the password version number? I didn't want to have to memorize what version password I was on for every site, so I'd need to keep it in a file somewhere, which I'd need to share between all my computers. (This was before I had any mobile internet devices, so I was only concerned with desktops).
And then I realized I needed storage for more than just the password version number, because I remembered all those idiotic password restrictions that so many sites like to use. Things would be a lot nicer if sites would just at least come up with a common format that they all accept in addition to whatever else they accept, such as 32 to 64 characters in [a-z0-9]. Then everyone using a password manager or password generator could use that format, and we'd all be happy.
But they didn't, so that means I'd need to store and sync some kind of formatting information for sites that cannot accept whatever my default generator format is. So, add that to the file that is storing the version numbers for each site that is past version 0.
And then I realized another issue. I have passwords I want to store that were imposed from outside. For instance I have a password share for the key to an encrypted database at work, made via Shamir secret sharing. I want my password management system to hold it for me, but not to generate it.
This could be dealt with. I could have had the password management system generate a password, and use that to encrypt my Shamir shared secret. Then I'd have to store that encrypted file somewhere that syncs to all my machines. It might make the most sense to build support for this into the password manager, providing a general "store a secret string" function, where it handles encrypting it and then stores it in the same place it is storing password version numbers and site-specific password formatting templates.
At that point, 1Password showed up in a MacHeist bundle, I gave it a try, and very shortly afterwards abandoned my password generator/manager development.
Master Password says it has password versions, password format templates to deal with idiotic sites, and storing imported password in the app encrypted using a generated password. What I did not see (I may have missed it) is an explanation of how this works if I have more than one device.