We agree and yet we do not.
Unless you are talking about times on the order of one nanosecond, the time it takes light to travel about a foot, (corresponding to a frequency on the order of 1 GHz), there is no way that the currents can be unequal at two different points in a single closed loop circuit. The electrons have to be going somewhere.
What causes the effects that you observe with spikes, inductive kickbacks, and other transients is current through relatively small stray capacitances that make no noticeable difference at 60Hz but become important at higher frequencies. So when I am talking about reactive current paths, I am including ones in the range that you would not notice unless you were specifically looking at transients and high frequencies.
Let's now assume that the exact same current waveform was applied through both windings of the GFCI current sensor. If the coils are not necessarily identical in characteristics across that wide frequency range, you could then get a non-zero difference signal. One simple way for this to happen would be if one of the coils has a little more intra-winding capacitance than the other, so some of the current at high frequency is actually bypassing the coil instead of flowing through it.
That does not change the fact that the same current is flowing in both wires, it just means that the GFCI is not well enough engineered to behave well at that frequency. And, as you point out indirectly, it is easier to use a time delay to ignore those signals than to engineer them out, especially if part of the problem is capacitive couplings within the appliance.
This delay takes care of both problems with one stone.