This is especially valuable when switching cms/erp/ticket systems etc where you may not have a lot of ability to manipulate generated links.
That's the value prop.
A perfect example would be the Scuba and OBS observability UIs. Instead of sharing a gnarly 500-character URL in chat to point someone to a specific query, you click "generate fburl" and get a short link.
More and more commercial/open-source software has built-in support for creating their own short links these days (Grafana and Kibana both do), but having it be ubiquitous -- and easy to integrate into new tools -- was really nice.
No need to find it on Google Drive (where the title may or may not follow consistent patterns) or remember which of the many Google doc links in autocomplete is the correct one.