Celestial navigation actually drove the development of accurate clocks
https://timeandnavigation.si.edu/navigating-at-sea/longitude...
Quartz clocks didn't overtake chronometers in terms of accuracy until the mid 20th century, and chronometers will still beat regular crystals like you'd find in cheap electronics.
> Celestial navigation actually drove the development of accurate clocks
That's true, but that still doesn't change the fact that you don't need nanosecond precision for this purpose. At the equator, 1 second precision gives you roughly 500m accuracy, which is already much higher than what the celestial imagery allows here (4km in the paper).
Clearly this method isn't limited by clock accuracy at all.