The way LLMs work is by approaching the most "average" response given any particular input. It's why everything written by an LLM looks similar and always has the same voice.
Anyways, shockingly, the Machine That Generates the Average Output is bad at unique passwords.
Of the 50 returned, only 30 were unique (20 duplicates, 18 of which were the exact same string), and the vast majority started and ended with the same characters.
Imagine that an LLM tries to fit its outputs into a bell curve of potential responses, with each character in the output aimed to be as close to the middle as feasible (with a small randomization factor so it's not always the exact same). A good password's bell curve ought to be a completely flat graph where any character is just as likely to be chosen as any other character.
Use a password manager.
I never understood the logic about not writing down passwords in your own home. If somebody can steal my passwords, I have a far more serious problem.
Just don't put it up on the pinwall in front of your webcam.
It's the kind of advice against a post-it note on your monitor (especially in a shared place like an office) but often gets over applied to all paper backups. I keep backup access to my password manager in a paper envelope with other important documents just in case.
My handwriting looks like a very drunk chimpanzee's. I can barely tell what I wrote an hour after I wrote it, let alone 6 months later when I'm trying to work out a password.