I thought I'd make an account on contribute on this issue as the author of a (probably pretty bad) password manager
https://slaymaker1907.github.io/password/, source code at
https://github.com/slaymaker1907/password-hasher.
There definitely is an issue with some websites having strange requirements, but the way I get around it is keeping an drive sheet with all information used to generate the password (except for the master password of course). This does add some state, but I find that for common passwords I memorize the method of generation very quickly.
There is a central point of failure if the master password is compromised. However, this can be mitigated by first choosing and memorizing a very strong master password as well as versioning passwords by storing the name of the master password used with the rest of the info (though obviously not the master password itself). Additionally, I find the threat model under which such compromises to not be very convincing assuming you choose a strong master password compared to the common case of simply needing to change a password key on the site from linkedin1 to linkedin2 in case of a password database breach.
One weakness of password vaults is that they don't have the advantage of working without access to the vault. While my method can store state as mentioned above, it is very easy to memorize this state, particularly for common/important passwords and has actually saved my bacon before.
Finally, something that I think is a significant strength to a manager but a weakness for managers is that I can and do use my manager for passwords that I need to type out, most often using a feature that translates the password into a password similar to a diceware password (I use a significantly shorter dictionary since dictionary length does not affect the entropy density of a password very much and it makes them easier to type/remember if only using common words). Using this feature, I've been able to create separate passwords for my desktop, laptop, and phone that are both easy to remember as well as having good entropy (when I compute entropy I do assume that an attacker knows the method of generation).