They don't want that because they don't want them to be automatically resolved so they can do metrics which is like 99% of the reason they are used in electronic form.
If they are temporary redirects, so not cached, they can do metrics from the server logs perfectly well.
Not if the intermediary, say, Twitter, de-shortens the link once, and then sends all the real traffic to the cached destination URLS. Not that they do that at the moment.