Users want to share or save links to specific resources discovered in a library database. These links are long and complicated, especially permalinks with a proxy prefix, and often get mangled if unicode is inserted. A URL shortener eliminates problems with sharing and embedding.
Shortened URLs may be blocked because of their use by spammers.
Users cannot troubleshoot a broken link from a shortened URL.
The shortened URL may expire.
Verify that the protocol, i.e. HTTPS, is compatible with shortening service. Access will be blocked to library resources if the original URL use HTTPS and the shortening service changes it to HTTP.
There are a variety of URL shortener services available, but some services like goo.gl have ceased operations. Check that the shortening service is compatible with your needs. These two services are widely used.