Kirchhoff loop law justification, and a rapidly oscillating circuit

Kirchhoff's loop law states that the sum of emfs equals the sum of voltage drops around a loop. In the electrostatic case, it would make sense in that the sum of potential differences should be zero around a closed loop. More generally however, we can have other sources of emf, like motional or chemical - in which case the justification for the law seems to be: the work required to move a charge around the loop is zero.

This makes sense if current is constant, as charge carriers stay at the same speed and hence cannot gain kinetic energy as we leave the circuit closed. However, it's not obvious to me that a charge cannot gain energy at all when current is changing. Say we have an AC circuit - is it not possible that charges are gaining energy when going around a loop? That would be consistent with the fact that the current is changing. Or is it the case that this "equilibrium" happens much faster than the current itself changes? What if we consider the limit of very high frequencies?

To build on that answer: KVL comes from Faraday's law, which states that EMF around a loop is equal to the rate of change of magnetic flux. If we can model the magnetic field as coming from an ideal lumped inductor, then KVL is exact, since the change of flux is accounted for by the inductor voltage $$V=L \frac{dI}{dt}$$. If there is some external magnetic field, or the circuit cannot be modeled with lumped inductance, then KVL is only approximate.