A possible answer to why the speed of light is measurable

The premise:

A recent Veritasium video suggested that the speed of light is unmeasurable due to the absence of experiments that could conclusively prove light speed is the same in all directions.

This is due to (according to Veritasium) having all known experiments that measure light speed done by shining a light beam at a mirror with a known distance and having the beam bounce back to its origin to measure the time it took to complete the round-trip.

These types of experiments introduce the possibility that light could travel at a different speed on its away trip than it would on its return trip, which confines the accuracy of those experiments to only measuring the average of the away and return speeds, and not the absolute speed of light in any given direction.

Here is the well made Veritasium video explaining the premise:

The answer:

My proposed answer is instead of using mirrors, let’s use a fixed interval pulsating light source circling an observer at a fixed radius with a steady speed.

If the observer detects fluctuations in the interval duration of the pulses as the light source travels around the observer, then the answer is yes, light does travel at different speeds based on its direction, otherwise light must have a fixed speed in all directions.