Whether you like this implementation or not, the solution is to choose better passwords.
If somemone (burglar / law enforcement / intelligence agencies) breaks in, they have your passwords.
If you are memorizing a lot of passwords (I have 500+ in my password database) you are surely going to forget rarely used ones.
If passwords are written down, they can be demanded from you by a warrant/court order. If they are memorized, they cannot.
If your passphrase is an innocuous phrase, like "red dogs like spicy food", how will they you know you have a password to demand? How do they know you have a piece of paper instead of having it memorized?
Previously I tried to memorize passwords. I ended up forgetting a lot. It was frustrating trying to remember what my password was, or even whether I had an account on the site or not. The user experience of being able to ctrl+f through all the accounts that I have in my database is very refreshing.
I have a quite high value video game account, and 6 people have specifically targeted me. They've attempted various things, such as trying to exploit password reuse, and utilizing previous website database breaches that I was in.
I don't see what benefit the paper would have. Whether it's paper or a password manager, if my computer is compromised they'll get my accounts with a keylogger.
I've never lost my wallet, but my brother lost his a couple months ago. I never really change my passwords except when I was switching from my old crap password to unique strong passwords in my database. The problem with losing my wallet would be that I would lost access to all my accounts if that was the only copy of the paper. It would be an availability problem.
The encryption scheme on iOS is nice, but for how much of a game they talk about privacy Apple had the opportunity to do so much more for security around identity/auth and they did approximately nothing.
I mean, I understand that computers managed by typical users will be a shitshow, but much of the problem in that situation is that they don't really care.