This is a common take on password managers but in practice it doesn't really hold, because humans are bad at security and good password managers are really fucking good at it. That's not to say there aren't weaknesses to the password manager model, but you're overestimating them and underestimating the ones in your scheme.

I also invite you to read my response above to someone else regarding the security of such an algorithm: with some examples, brute forcing an algorithm is easier than brute forcing a master password.