Is there a fundamental limitation on how rapidly (with voltage) can a diode ’switch’ ? If so, can you pinpoint its origin?
A diode is "on" when there are charge carriers in what is normally its depletion region, and "off" when the depletion region exists.

Therefore, the fundamental limitation on switching speed is how fast those carriers can move into or out of the depletion region. This relates to the mobility of the carriers and the magnitude of the E field across the region.

The capacitance of the junction itself, along with any stray (parasitic) capacitances put a limit on how fast you can cause the E field to change in the first place.