A (well handled) physical password booklet is much more secure for the average home user, who is unlikely to ever be individually targetted by a third party attacker, let alone to the level of the attacker physically breaking into their home. My parents being victims of a zero-day vulnerability or installing a malicious application by mistake are much more realistic scenarios than their house being broken into and their password booklet being stolen by a thief who is meticulous and observant enough to take it and know how to make use of it.
Not only that, I would argue that a physical booklet is not only more secure but also safer. Nothing short of a house fire will destroy the booklet, and however much I like to rave about old-school ThinkPad durability, I don't think my locally stored encrypted database would survive that either.
A password booklet works well at home, but it's obviously much less secure if you wanted to sign in to a service while in public on your phone for example. One of the major benefits of a password manager is that your passwords are present, encrypted, on all of the device you need them on. Most people don't only need passwords at home, so the odds of theft or loss of the password book are much higher than your example makes it out to be. If we're talking about an average user, the solution of only sign into services at home isn't really an option.
You are correct that the access security of a booklet is almost certainly better than that of a password manager. The issue with the booklet is that humans do not like transcribing long strings between computer and paper so (at least in my experience) people who use the booklet method tend to eschew longer passwords, they tend to avoid creating new passwords when they can re-use an old one, and they don’t change the passwords very often (if at all). Also in the event that the booklet is ever lost or stolen (which is made significantly more likely by the fact that you must carry it around with you everywhere in this age of the pocket computer), you are suddenly in a very bad place.
Not only that, I would argue that a physical booklet is not only more secure but also safer. Nothing short of a house fire will destroy the booklet, and however much I like to rave about old-school ThinkPad durability, I don't think my locally stored encrypted database would survive that either.