Another use class is to change all links to open in a new tab by setting only "target" on the <base>. This happens on marketing sites with a lot of third party links so the marketing department naturally wants those links to open in a new tab instead of the current tab.
However, this can create a vulnerability as the linked website now has a reference to your site through window.opener and can take the user away from your site:
https://www.jitbit.com/alexblog/256-targetblank---the-most-u...
Also, if ever use relative urls for assets or requests, and you deploy to different URL's (or your deployed URL path's don't map 1:1 to your filesystem paths), it can come in handy.
Angular also uses this to determine where the client side routing begins - https://angular.io/guide/deployment#base-tag .
Admittedly this is probably not the use case you're looking for.
I'm unsure if there's any utility to publishing a publicly-visible page using this tag.