This is a historical quirk. “Flight Service Station” is nothing more than a 1980’s (or late 70’s) name-change for an animal that was known simply as the airport radio station. The operators were known as “radio operators”, officially licensed under international rules, and the site would be called “Brandon Radio”, or whatever. Back then, most airports of any consequence had one.

The job morphed somewhat as communication facilities for ATC centres improved drastically, and things like ATIS came to be. Perhaps the importance of “xyz Radio” as an extension of the old ATC Centre’s limited-range VHF diminished somewhat, but the basic provision of weather, flight-plan-acceptance/termination, and air-ground communications remained.
Transport then tried to highlight the “service” aspects of the job, rearranged the responsibilities a little bit, and changed the name to try to improve the image.... . 
Back to Radio Communication Commentary