What advantages are provided by an unstable canard configuration for fighters?
You want your control surface to create only little lift, so it has enough margin for maneuvering. This confirms your first guess.

Your second guess is also correct: Flying supersonically shifts the center of pressure back and increases stability. If the aircraft is unstable subsonically, it will suffer far lower trim losses supersonically.

Please read all about unstable designs in this answer. For conventional, stable configurations it makes most sense to put the control and damping surfaces at the back, and a canard is the better choice for unstable, highly maneuverable aircraft.