Earlier quoted context omitted.
Which is exactly how the telephone industry has done it for decades, it's called a "building-integrated timing supply", or BITS clock. Typically this is a GPS-referenced clock with a local quartz or rubidium holdover oscillator, and output cards with dozens or hundreds of outputs serving various machines in the office.
Curious, why did telephony require such accurate clocks?
My signals background mostly comes out of music, so somebody else probably has a better answer. But any time you need to convert between digital and analog signals relatively seamlessly, ie, introducing minimal processing overhead, you’re going to run into these kinds of issues. In that regard, you can think of telecoms as a CPU, and just like in a computer, you need a system clock that the entire architecture agrees on.
First likely application that comes to my mind is VoIP.