Earlier quoted context omitted.
It's not drift. Time passes more quickly on the moon, to such an extent that there are 56 microseconds more each day on the lunar surface than on Earth. This is a an effect of general relativity. For everyday human-scale stuff, sure this doesn't matter. For precise scientific and industrial use cases, it does.
I repeat myself: What's the difference between taking a good clock to the moon, where it runs 56 microseconds fast each day, versus having a less-tuned oscillator that runs 56 microseconds fast each day?
It's not just about keeping time on the moon. It's reconciling that with other places in the solar system