While putting it together I stumbled upon the following quote in the NTP Faq
Time usually just advances. If you have communicating programs running on different computers, time still should even advance if you switch from one computer to another. Obviously if one system is ahead of the others, the others are behind that particular one. From the perspective of an external observer, switching between these systems would cause time to jump forward and back, a non-desirable effect.
As a consequence, isolated networks may run their own wrong time, but as soon as you connect to the Internet, effects will be visible. Just imagine some EMail message arrived five minutes before it was sent, and there even was a reply two minutes before the message was sent.
Even on a single computer some applications have trouble when the time jumps backwards. For example, database systems using transactions and crash recovery like to know the time of the last good state.
Therefore, air traffic control was one of the first applications for NTP.