If all accounts would have sane restrictions on the password it would become trivial to have something both secure and convenient. I have been looking for a system that allows me to: 1. Does not require me to remember an absurd amount of information. 2. Allows me to login to services, even from other devices. 3. Has a unique password for each service (so that it is not disastrous if one password leaks).
We could have one master password, use site and username (and maybe a counter, to make it easy to rotate passwords) as salt, and use a hashing or password derivation algorithm to derive a unique password for each service. This would only require you to pick and remember a strong master password.