And what purpose does it serves? An additional layer of security/safety? A strong password is a strong password, why load the brain with remembering public and private keys. I have a word document dedicated to copy paste all the different passwords in different sites. I have to be a memory man to get through all these without the doc.
If you are using a weak password you would get hacked one way or the other, if you are using a strong password you are immune to hackers, it's as simple as that.
By strong password, I assume you are referring to BIP038? I agree, if you want a paper wallet that has an additional layer of protection in case it falls into the wrong hands, that's a good way to go.
Brain wallets are only useful if you do not want to print or store anything other than your public address. In the example I gave, you do not have to remember anything but your phrase (you can have a modified one for each public address), and a strong password which you can employ as a SALT for hashing your phrase.
Your word document with different passwords must never fall into wrong hands, e.g. someone who hacks your computer.
In my case, they would have to pick my brain ;-)