ORIGINAL: BFoote
Reason F-16 uses its horizontal stabilizer to fly on is because of the huge parasite drag at high airspeeds, thus if you balanced the fighter the same as say a Cessna 172, you would have the horizontal stabilizer doing nothing but creating Parasite drag and a bit of Induced drag etc. Take that same horizontal stabilizer, load it up, decreasing the load on the main wing which decreases its needed angle of attack decreasing induced drag and pressure drag at high speeds creating an overall best L/D ratio of the entire plane with set amount of thrust from the engine.
While reducing drag by shifting CG will increase top speed, I really don't think that's the reason for the F-16's CG location. The neutral point of an aircraft shifts aft when supersonic. If the neutral point shifts aft but the CG does not, static pitch stability increases. An increase in pitch stability reduces pitch authority. To preserve supersonic maneuverability, the CG of the F-16 is located such that stabilators lift upward when in straight and level subsonic flight (and the airplane is statically unstable in pitch). An F-16 is operating nowhere near its L/D max when at its highest speed.