This is written by a theorist so they do leave the important bit out. Of course, you know just from fourier analysis the uncertainty principle. The thing is treating photons as plane waves is an approximation (a fine one for most things, particularly theoretical calculations). A better approximation is thinking of photons as wave packets that thus have some localization but not so defined as to make their bandwidth too wide (so they can be considered monochromatic).

The important thing to remember is that photons, like the very idea of a planewave is always an idealized approximation.

Btw. I have an impression that time- and place-local behaviour can be modelled as a collection of photons that destructively interfere "elsewhere" than where we tend to actually see light. Fourier transform seems to play a big role here.

Your statement is not very rigorous, but the intuition it provides is spot on. It is pretty much exactly this intuition I convey the first time I teach such topics.