Or should this be more specific in that you shouldn't shorten URLs using the provider's domain name, but bring your own domain. So if the provider goes away, you can in some way migrate the links.

As a hypertext purist, I used to think this. But working for a large organization, shortlinks can be an invaluable way to actually maintain the integrity of links that have been deployed to unrevisable media (emails, print, pdfs, etc).

If a resource has been relocated off of a host/url, often part of that situation is that we don't have immediate access to implement a redirect from that host to the resource's new location.

Now I see a shortlink manager as a centralized redirect manager, which is so much more rational and stable than creating a tangle of redirect config across dozens of hosts or hundreds of content applications.

The caveat is that you don't need to use a 3rd party domain or service, you should definitely at least use your own domain. You also don't need to make them unreadable hashes, they can actually be more human-friendly.