This is why complex passwords are totally and utterly flawed anyway.
Even in this day and age there are sites where the backend doesn't use a particularly strong password system i.e. limited length hash where multiple passwords will match. Bit less usual these days but I know some still do.
I find 2FA a pain in the rear, every site seems to have a slightly different implementation and while the security from other people is much higher so is the chance of locking yourself out of your account forever.
Please tell me that doesn't mean it's written down on a scrap bit of paper in your wallet or desk drawer.
With 2FA systems you often have to store back up codes somewhere as well... (well you don't strictly have to but it is a good idea to have a copy of them).