I imagine search history data is used to facilitate and optimize repeat searches, e.g. repeatedly looking up your secret crush or exes.

It does actually... there used to be a way to pull out what people facebook "ranked" highest for you above others. That's why search isn't always alphabetical when you use it, it sorts the list by a preference score they generate based on how you interact with profiles

The search box in the UI is populated with your last dozen-or-so searches. You can access that data about yourself, so presumably if someone has the ability to "view as" you, they can see it.