If a user pastes some JSON, clicks the Access URL text box, presses Command-A Command-C to copy the URL, then pastes it to someone else, that person won't be able to open the URL, because it lacks a "https: prefix. That's probably a bug, whether or not it's an intended feature.
It's not something that matters very much, but your users might be slightly annoyed at having to chop off the leading "//" every time they want to copy the URL.
I admit I might be missing something obvious, though.
I didn't expect it to be a service for freely hosting data -- that's pretty cool. I assumed it would return a rate limit error if you tried to use it for anything substantial.
(I missed the About link https://jsonbin.io/about at the bottom, which explains all this.)
By the way cool service. I've got an internal JSON store service too and it's super useful for a number of purposes.