Why power system frequency is determined by load

To be precise, the frequency of a power system is determined by the active power.

From the abstract concept of a system of all generators can be equated to a generator, this generator is pushed down by the prime mover to rotate, the generator's active load is expressed as a rotor torque resistance, when the prime mover torque and resistive torque balance when the rotor speed is stable, the frequency is stable. When the load increases the resistive torque increases, the rotor decelerates, which is manifested as a decrease in frequency. Conversely, when the active load decreases, the rotor accelerates and the frequency increases.

Reactive power currents are not forced in the magnetic field, so they are independent of frequency.