We don't think of it as storage - although you can indeed use it as such. We think of it as messaging. Oh By gives you a way to send messages to unknown people at unknown future dates which don't require any special tooling (apps) to decode.
You can just take a piece of chalk and write your message on the sidewalk.
As for longevity, I think we have a good track record having run rsync.net for 16 years now.
Close. It is an everything shortener.
URLs are indeed something you could shorten, and I would argue that it is the best URL shortener because it has no javascript, tracking, login, etc. and no ads/delay on redirect.
But I don't know how relevant or useful URL shortening is in 2017.
As for logs of accesses, you are right to be cautious and be mindful of your risk profile / threat model. However, it's worth noting that you can create Oh By Codes completely anonymously.
"Twitter for pastebin" - thanks, that's a good line :)