Keep in mind that most password managers also encrypt your password database with your master password, so my solution isn't any worse than those.
Memorizing a even a 16-character (upper/lower + symbols) random string as your master password would be 16*6 = 96 bits of entropy which is more than enough.
Dealing with memorizing ONE good 16-character random string is within the abilities of most people. Dealing with multiple ones is what is hard.