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.
> a way to prevent random connections from having keyboard access if I were to forget to unplug
Pretty sure that already exists, at least on Android. InputStick lets you set up a pre-shared AES Key and pairing PIN that you need in order to connect to the device.
Sounds like someone isn't using a 100-character randomly generated password.