It's not about accuracy (nobody really cares if the whole network is running fast or slow compared to some other clock) so much as synchrony (the whole network needs to be running from the same clock).

Asynchronous networks can't guarantee latency or jitter performance, and they require buffers. Synchronous networks (remember, this is voice-grade stuff) can deliver bits out at the same rate as bits in, anywhere in the network, without dropped frames or stuffing or anything obnoxious like that.

Analogy time: If all you're familiar with is packet-switched networks, sure, let's call them trucks. A truck gets filled with payload, it leaves, and sometime later, it arrives at its destination. Packets get reordered, and it's someone else's problem to deal with that. A great many shipping-and-receiving docks contain a great deal of complexity, to check bills-of-lading against what was ordered, with warehouses to smooth over the difference. It works today because computers are powerful, and buffer bloat is still a plague.

Implementing VoIP with 1960s technology was... not practical.

So, synchronous networks don't require any of that complexity. Nothing's ever out of order, there's never a bit arriving too soon or too late. You don't even handle them as packets, they're literally just streams of bits, coming out of an ADC here, beating through the network in synch, and being shoved into a DAC over there. Rather than a truck, imagine a bunch of slow conveyor belts feeding a faster-moving belt with a spinning turnstile or little paddle controlling what goes onto it -- for this microsecond, input 1 can emit a bit onto the belt, then a microsecond later, it's input 2 and so on. So the belt contains an ordered stream of bits, and at the other end there's another paddle spinning in sync with the first, demultiplexing the bits back out to their sub-rate circuits.

This can be implemented with discrete transistors. There's no need for buffers or packet reordering or any such nonsense. And definitely no repeated frames. There are no hiccups, no dropped frames, no reassembly or reordering. And definitely no repeated frames. End-to-end latency is the speed of light plus one half a frame time, on average.

And if you can make the whole continent beat in sync, you can enjoy this level of service and predictability even on long-distance calls.

Initially (in the 1960s, as time-domain multiplexing was deployed) this was done by having one master oscillator in Kansas City (the approximate geographic center of the continental US), and fanning-out its timing through an enormous branching-tree structure of amplifiers called Synchronization Distribution Expanders. This performed beautifully but it was a logistical nightmare, any network disruption could cause problems, you needed local oscillators for holdover anyway, etc.

As GPS was made available for civilian applications, it made sense to convert to using Schriever AFB as the master clock, use the space segment as the distribution network, and simply give each office an antenna to tap into it. The implementation is a bit tricky because of doppler shift and stuff, but GPS receivers abstract all that away, and can hand you a timepulse which is synchronized to GPS system time. (Then the BITS rack converts that to the useful frequencies and distributes it within the office.)