Once you need to keep track of extra information like that in a google doc, how is that better or more convenient than just using a normal password manager with a vault?
It's free, you can print it out and tape it to your workstation, etc
The biggest problem with password managers is that you become completely dependent on them (and therefore completely helpless without them) once you start using them. This scenario still allows you to remain decoupled from that dependency.
If you use a vaultless password manager like GoKey you're also going to be "completely dependent on it" (and a printed copy of your list and a copy of your key if you're using a key rather than a master password) to log into anything. Why is that better than being "completely dependent" on another free password manager like Pass that's just a wrapper around gnupg and git?
In either case you're going to need a copy of the software itself and some sort of shared file with either a list of password changes/rules, the actual encrypted passwords, and a master password or key to log in to anything.
Once you've given up on being able to log into sites without having a specific program handy and synchronizing some sort of data, why not simply store the encrypted passwords in the data you're synchronizing?
I disagree. I use a vaultless password manager and I have the metadata for my most common accounts (Google, Amazon, etc) memorized so I am not completely dependent on the metadata file. The vaultless password manager can easily be downloaded anywhere, and could even be manually implemented if need be so I'm not completely helpless without my phone unlike my PM friends.