So what happens when you need to change your password because Cloudflare dumped your session to some other user? They can now get in to your account unless you come up with a new algorithm which you have to remember alongside the original one, on top of which you need to remember which accounts are using which algorithms.
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No, you simply change your passphrase. Even if you write those down in an open list, no one can use them unless they also know your algorithm and your special characters. So when you go to an old page, you just try the old passphrases and then change it to the new passphrase (keeping the same algorithm). But you should change all your passwords on a schedule. With this, that becomes less of a problem so you are more likely to do it.