The airbase is definitely not unhappy about the exposure it’s been getting through the anime, and even used Girly Air Force art to promote their annual air festival held at the base each September.
The Komatsu base is the only Japanese airbase on the Sea of Japan coast, making it the logical main setting for Girly Air Force, as that’s where the Xi have been attacking from.
In Girly Air Force, humanity gets overwhelmed by a mysterious alien force called “Xi”, whose aircraft are far superior to mankind’s conventional weaponry.