Does the physical size of through-hole ceramic capacitors relate to voltage rating?
For a big capacitor the distance should be low and area should be high because capacitance is directly proportional to area of the plates and inversely proportional to the distance between the plates. But if the distance is too low, the dielectric will get punctured with voltage. So there must be a proper distance between the plates according to voltage; and for that distance, the area should be high as to get the required capacitance.

So in any capacitor, the size depends on voltage and its capacitance value because voltage rating is proportional to distance between plates and capacitance is proportional to area of the plates.