Maybe silly question, why we care about nanosecond speed, don't we only need to sync once and the other system can count the time by itself?
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Most clocks drift. If you've ever used a normal watch (not a smartwatch connected to a phone) or a battery powered clock, you may have noticed that you need to correct the time every month or so, as by that time, it's lost accuracy.
The problem is due to the quartz oscillators these devices use, which are the same ones we use in phones, computers etc., which have the same problem as a result.
You don't notice this because just about every network-connected device these days uses NTP or something similar to keep its clock constantly up to date, but the clock itself is still inherently inaccurate.
There are also other mechanisms to keep clocks in sync by the way. Some mains-connected devices keep time using the 50Hz/60Hz mains voltage. Various countries have radio broadcasts that devices can be used to keep time (DE, US and JP run them, I believe).
Why care about continuous sync? When I was in small robotics startup we had a separate motor controller driving each axis. A customers complained that the precision was getting worse after running for a few days non-stop. Guess what? Each axis had its own CPU clock based timer defining how long a segment should take. The difference is negligible but it accumulates over time. It was no issue for other customers who had a pause somewhere in their motion.
Why nanoseconds though? Usually a sub-microsecond sync is good enough. I can only think of some specialized phase measurements, really, like when you need to know from which direction a radio signal is coming based on timing of two antennas.
A quartz oscillator drifts by roughly a second per day.
(Edit: Bad math left my underestimating by a few order of magnitude. Whoops.)