One function that is harder to do without a database backend, as static sites don’t, is search. With WordPress, search is baked into the core and all templates have to do is not get in the way. But on a static site, there is no backend to call, no infrastructure to invoke, and no user interface to show.
Static sites have gotten around this by using third party search providers. Basically, you add some third party code to your site and then magic happens.