A current spike in an Inductor? I believe this is physically impossible.
Nearly correct.
K is physically unrealizable. For the same reason:
A clamp or snubber would usually be added across the transformer primary whether the spike was caused by reverse recovery of the rectifier or not, because leakage inductance in a real circuit will cause a primary spike anyway.
doesn't matter here, as there's no leakage to cause voltage peaking, but a real flyback with nonzero leakage will have voltage spiking on the primary side turn-off, and secondary side turn-on.
Voltage peaking does not show here, because there's no leakage to generate it.
But current spiking is real
and finite, because even in absence of loop inductance, transistor dI/dt is set by gate drive characteristics (and any parasitics in the device model if applicable).
Tim