Yes, there is a purpose to "static" characters; in plays and movies we call them walk-ons or extras.
Static characters are not statues; they are just people that, for the story, do not change. They are who they are, from first appearance to last.
In many cases a static character provides some conflict or humor. The cabdriver that can't stop talking about what species of butterflies he has photographed and where. Or the customs clerk that won't let you into a country.
Other times, they are just there for realism; if you are going to a modern airport, you don't just jump on a plane, it takes an hour and navigating a crowd the size of a small village. Standing in lines. You will probably have to converse with some of these people. If a character visits a doctor, the entire staff is likely static, doing their job for the day.
So they are not only static, but one-dimensional; barely an outline of a person revealing nothing of their inner life or any hint of why they are where they are at this point in their life -- she's just a doctor, 45, fit, in a white coat.
Depending on your story, parents, siblings,teachers, coworkers and other recurring characters can be static, they are who they are, you just need them there for the realism.
And finally, there is practicality: There is limited space in a book, film or play, even limited scope in a TV series. There just isn't enough room to give all characters a story arc, growth or decline. There is even limited space in the audience; give them too many story arcs to keep track of and they cannot; the story becomes jumbled and confusing, they lose track of who's who and stop caring.
Stories are about journeys of change, for one person or in the relationships of a small group. Family, coworkers, business partners, etc. Even in popular TV series, we seldom expand that "group of change" beyond about a dozen. There, we have the time (literally speaking) to accommodate this; a good TV series can have the collective viewing time of over a dozen feature-length films and thus that many more character story arcs.