Ohm's law:

Impedance, as you know, stays basically the same for the test as its simulated shorted to ground on the secondary side. Then, if you reduce the voltage, what has to happen to current? That is the current you plug into that power equation. So KVA is not constant.

The KVA max OUTPUT staying constant at a large primary voltage range above percent impedance voltage is due to saturation and is outside the original scope of the question. It requires higher math to look at as primary impedance actually does change in this scenario (See SCPT or magnetic amplifiers at your peril).

Again, at a tech level with one dependent, one independent, and one fixed variable, KVA will not be constant and power in will equal power out(unlike in saturation).