Writing down a password is simpler, but it is also stopped being reliable for the vast majority of users because it stopped being adequate security for the average user. Passwords are too easily stolen. Passwords are too easily reused because human memory is quite fallible. Passwords are too easily caught by a man-in-the-middle attack or a social engineering attack. Passwords are too easily leaked in a database breach. Even when properly hashed and salted, password hashes still are weak to rainbow tables and other such attacks.
Passkeys trade off a bit of supposed simplicity (if you ignore modern advice like use different passwords for everything and always use a password manager because you will never remember all your passwords, it's not humanly possible if they are also all secure enough passwords). But the tech is already at a very usable level of simplicity for average users. It's just like learning a password manager. For some average users it is even easier than learning a password manager the standards and standardized user flows have simplified a lot of the hard edges of the password manager, including the above mentioned "use a QR code to provide temporary access on some other device to your Passkey without syncing your full Password Manager".