It's funny, writing passwords down is excellent advice on today's Internet.
Physical security is easy, who's gonna see inside your purse? How often does that get stolen? Phones and laptops are high-value targets for thieves, and if they're online there could be a vuln. Paper doesn't have RCE.
(That said, I use KeePass, because it's nice to have it synced and encrypted. These days only my KeePass password is written down.)