There are some sites that have receiving implemented but not sending, and it was primarily meant for that. (This is probably most often people who are using webmention.io as their proxy endpoint by registering and adding a line of code to their header. Something I do with both a TiddlyWiki and MediaWiki installs that don’t have custom software/plugins yet.)
It also serves to help visually indicate that your site supports the protocol if you don’t have a button/badge for it that points to something like https://mike.rockwell.mx/wp-json/webmention/1.0/endpoint. For those that care or are in-the-know there are manual services like https://telegraph.p3k.io/send-a-webmention or http://mention-tech.appspot.com/ which could be used as well.
On some sites I follow, I use those boxes about once or twice a month. I use it a bit more frequently on my own site to manually send myself webmentions from other sites that don’t send them, but which I come across either randomly or via refbacks.