You probably know these facts:

• Long, random, abstract passwords are better than short specific ones, at least 16 characters, and some places are recommending 24 now!
• Hackers know about changing O's or o's (Ohs) to 0s (zeroes), or Es to 3s, or As to 4s or @s
• Using the same password for banking as for social media means that when the social media data is hacked, your bank access is also compromised
• Memorising a different 16 character password for every site you log into is not possible for most of us

So we all need a system where we can safely store random passwords for everything we do that requires passwords. The simplest of this would be to carry a little-black-book, and as long as you do not lose that book, this is a very good idea.

I disagree with the statement "you shouldn't write down your passwords", rather I think the statement should be "You shouldn't leave your passwords written down by your device".

If you have your passwords written in a little-black-book, and you carry it with you everywhere you go, and never leave it by one of your devices, that's far better than using the same password for every site, and better than most password managers but not better than 3rdKey.

But finding the password you need can be difficult, especially if you have hundreds of passwords. And it will get worn out, and you risk losing it.