Once upon a time, there was also the Soviet propaganda effort in the West. Many of the Cold War reactors could be used to produce not just electricity, but fission material for nuclear warheads. Meaning that if you could persuade big countries to give up nuclear energy for good, you'd also reduce your adversary's capability to build and maintain their nuclear arsenal, or preempt its future acquisition in the first place.
Soviet Union (and later Russia) enacted the propaganda effort against nuclear mainly to prevent the west from ditching their fossil energy. Less western nuclear warheads was secondary goal at best.
Military forces never had any problem running extra reactors to acquire their material.
Correct, but it still was framing that would be useful to have. If nothing else, because civilian reactors mean there's also a civilian program, an educational program, and the military would like to have that around.