Why is stabilator used in some small airplanes?
Simplicity. Yes, a servo tab is helpful, but most control surfaces should include a trim tab, so this can double as a servo tab. Total part count should still be lower than that for a stabilizer-elevator combination. But there are other advantages: Easier adjustment of stick forces and little loss of stability with free-floating controls.

By hinging the stabilator (or full-flying tail) near the quarter point, its control forces can be kept small and tailored with the servo tab. Also, this helps to keep the hinge moment coefficient derivative over angle of attack $c_{r_\alpha}$ low. The ratio between it and the derivative over deflection angle $\eta$ determines the angle to which the control surface will float, and a small $c_{r_\alpha}$ means that the stability with a floating control surface will be close to the stability with a fixed surface.

Also, balancing masses are easier to place when the full surface moves.