Maybe it's stupid, but the scenario I always have in mind is one from "Bourne Identity" movie, with Jason Bourne found in the sea, with nothing on him, no wallet, no phone. And it's not far fetched scenario either: I travel a lot, internationally, so I always imagine being mugged, having my phone and wallet taken away from me. Being able to login to my accounts, and more importantly, access my money in the bank with nothing but a password stored in my brain is important to me.
For services with TOTP you can store the secret in that encrypted file, so you can reload it back into your authenticator app. Or you could just use a Keepass file or similar which would store all the passwords and keys in a single encrypted binary.
Though you do have to be very circumspect in choosing that app: the news of Authy's desktop app (which you could pull the tokens from) being discontinued is still fresh in my mind.
Properly using a password manager provides unique passwords per domain too.