Depends on the security of the service you want to use - I'd expect my bank or my email provider to send me my encryption keys by a recorded letter. Hacker news can probably email me their key instead.

Again, we're talking about some "world ending" scenario that OP mentioned - where all "normal" forms of encryption are already broken. If OTP is the only unbreakable encryption around, them I'm sure we'd find a way to distribute keys.