Why most of the supersonic or fighter aircraft use all-moving control surfaces?
The biggest two reasons to have a stabilator (the most common all-moving control surface) are stability at supersonic speeds and increased maneuverability.

As an airfoil approaches its critical Mach number, the diverted flow moving past the wing's leading edge, because it has to move faster than the wing itself to follow the contour, starts to exceed Mach 1 and then decelerates below it, causing a transsonic shockwave to form behind the wing's leading edge. This shockwave causes boundary separation of the airflow at the trailing edge of the wing, where traditional elevator surfaces are placed. This reduces the wing's lift and also the effectiveness of elevator surfaces, a phenomenon known as "Mach tuck". By instead moving the entire control surface, this problem is avoided as the entire airfoil, regardless of the quality of the flow of air over any point of it, is used to direct airflow and thus rate the aircraft's nose.

Second, and more intuitively, the larger the elevator surface, the more air it redirects and thus the more force it places on the tail section, in turn allowing the pilot to pitch the aircraft at higher rates. The ideal endpoint of this line of thought is that the entire stabilizer also becomes the elevator surface; a "stabilator".

Both of these considerations are critical to the design of fighter jets, which as of the fourth generation were almost all capable of Mach 1 (and a few could exceed Mach 2), and which also have to be highly maneuverable even as the moment of inertia of the airframe in the pitch plane increases (an unavoidable side effect of wrapping an airframe around two high-performance jet engines traversing the length of the fuselage).