20 random characters typable on a regular keyboard have a little over 126 bits of entropy (electrum seeds have 128), so if you're going to do this you'll need to be strict about non-randomness of qualifying passwords.
Passwords suck, passphrases rock, they have a much better rememberability/entropy ratio.
With a 10 words passphrase you get approximately the same entropy as your 20 characters passwords and it's much easier for a human brain to remember, we're simply wired that way.
Like you said the quality of the generation process is of utmost importance.