In General you can assume that most of the Controlers are not familiar with military aviation. My experiances with live ATC are unfortunatly very poor regarding military flights. There are some exceptional good Controlers, but most of them either don’t care about military needs, or hat it. Don’t expect to much when flying a fighter jet.
Regarding your special case, the Controler might have judge you by the ICAO Size class the F-14 is in. The ICAO Size Clases A to F are related to Wingspan and Wheeltrack. The F-14 goes into class B with Wings foward, which is the relevant mesurment fore ground movment. With Wings swept back it fits into Class A, resulting in the “Light Aircraft” Category in IF.
Yes, that sounds stupid. And, yes it is in my opinion.
No, none of the Fighters in IF are Light Aircrafts. There are some light military aircrafts in IF, those are C209 Iraq Army, TBM French Airforce, and C172 CAP. All other are not light, but many are ICAO Size A.
The major issue is that IF is designed primarily for Civil Aviation. It often stumbles when it comes to military aviation. I do not expect that that would change to much. It might improve, but it would always have some flaws for Fighters…
This should go into ATC in my opinion.