The disater plan is to have a few dozens stratum 1 servers spread around the world, each connected to a distinct primary atomic clock, so that a catastrophic disaster needs to take down the global internet itself for all servers to become unreachable.
The failure of a single such server is far from a disaster.
And the disaster plan for the disaster plan is to realize that it isn't that important at the human-level to have a clock meticulously set to correspond to other meticulously-set clocks, and that every attempt to force rigid timekeeping on humans is to try to make humans work more like machines rather than to make machines work more like humans.
For those of us near Boulder, it's urgent.
But the stratum 1 time servers can shrug and route around the damage.