The physics of radio wave propagation are surprisingly complex. Buildings and objects in the path between transmitter and receiver can cause various interference effects that basically slow down the signal. I'm glossing over a lot, but it would take significant effort to precisely measure the exact delay between any one receiver and the transmitter. It's much more complicated than just the distance, and each one has to be measured individually.

I'm not an expert in RF, but I think this concept of a single synchronizing transmitter just doesn't work in the real world. You'd probably build a cell network with many transmitters covering small areas. Each transmitter has the hardware to synchronize with thr others, and the lights just have a simple circuit slaved to the transmitter clock.

There's probably more clever ways to synchronize signals over long distances, but RF is black magic to me.