Disregarding security of this particular implementation and trade offs, the problem is that while it's a simple solution, it's not convenient: password managers are more usable. I'm saying this as a guy who wrote similar password generator once, and used it for some time, then switched to a password manager.

When you need to change a password for some website, you'll have to add something to your "door id", e.g. a counter. Then you'll have to remember such counters for every website where you decide to change password. Due to this I was a bit reluctant to change passwords, which is dangerous.

If you want simplicity, the simpler and more convenient solution is to keep an encrypted text file.

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As for security, the best approach to deterministic password generators I've seen is this:

http://www.cs.utexas.edu/~bwaters/publications/papers/www200...

(Today you'll want to use scrypt as the hash, though).