Password managers don't help when you need to log in to a computer you don't own, e.g. a public computer at a library or office. Using password managers just makes it easier to lock yourself out when you need access most.
With mixed-case letters and digits, all you need are 22 characters.
A 128-bit security margin is considered good enough currently; a 62-character alphabet (26 lowercase, 26 uppercase, 10 digits) provides 5.95 potential bits of entropy per character; thus a 21.50-character password would provide 128 bits. You can't have a fractional character, so … 22 characters.
Typing 'tgcSq08O2fEZ5hcZk3Gvgk' in from a screen is easy enough, although not something I'd want to do every day.
Though I think 100 random characters is well beyond the point where you're no longer significantly increasing security by adding more characters. You can easily get 130+ bits of entropy with only 20 characters, and even for a ridiculously weak hashing algorithm like MD4 that'd be enough to withstand the entire combined strength of the Bitcoin mining network attacking your password for well over a billion years.
This is the solution I've come up with as well. It's saved a lot of frustration already, which builds up quickly with when you have to retype even a 16 - 20 character random password over and over again in a short period of time. I only wish for a better iOS experience and direct integration with 1Password. Oh, and a way to prevent random connections from having keyboard access if I were to forget to unplug.
Perhaps I'm overly paranoid. A public PC could be infected with god-knows-what malware that siphons off whatever that text is entered or rendered in a page or on the screen.
I wonder if there's another way to solve this problem. For example, a plug-in that would store cookies as opposed to passwords - and then "populate" a new session with existing cookies to log you in transparently.
More of a security nightmare than passwords? Maybe, though I can't see why...
Anyways, yeah I thought about binding auth cookies to some kind of persistent hash, although I'm not sure what it could be... IPs change (laptops moving), so do user agents (browser upgrades)... I guess I'll need to test this!