You can keep a physical password book. For someone to get it, they need to physically steal it. If you keep it at home in a fairly safe location, it seems fine to me.
If someone breaks into my home, they’ve got it. But that’s not a threat model that scales, so it’s not a major concern to me.
>You can keep a physical password book. [...] If you keep it at home in a fairly safe location,
But people are often away from home and want to log into websites and apps from their smartphone. A physical password book sitting at home is useless for that very common scenario. That "login from anywhere" is the typical motivation of gp's comment: "How can I keep passwords on 2 computers, an iPhone and iPad all in sync?"
If someone breaks into my home, they’ve got it. But that’s not a threat model that scales, so it’s not a major concern to me.