The main reason NEMP (nuclear EMP) became a big concern during the Cold War is its potential for use as a defensive weapon. For example, a large part of military EMP research was done with the specific aim of hardening strategic bombers, after it was realized that the USSR could use a single well-placed high-altitude NEMP to disable most of the SAC fleet as it passed over the north pole. Similarly, in most attack scenarios the USSR would almost certainly have made a high-altitude detonation over the ICBM fields one of their first moves.

I started off on a more detailed explanation of the timing issue, why we may not be able to launch before inbound weapons arrive, but it's kind of a complex topic that changed quite a bit over time. I might write something more in-depth about it later.