let see for benefit and disadvantage of Nuke on Moon
The Moon got low gravity field, mean you can launch the Warheads with smaller stage
The warheads take some time 3-4 day to hit there target, so allot time to evacuated the target's
You can take bigger rockets to make the Warhead faster, so it hit targets in hours
but you need very very big heavy Launch rocket to launch that mass to the Moon save without disaster.
ABM defense is easy against missile from Earth to Moon, because there slowing down until the moon gravity pull them down.
the Warhead dashing down with around 11 km/sec or even more, what make ABM from Earth difficult.
Attacking the lunar launch site is problematic, it dig under lunar soil, so a nuke detonate on surface has little effect
do lack of atmosphere like earth, so the Nuke must be a big "bunker buster"
who penetrate deep in lunar soil before it's detonate.
Except they used Mass-driver ala Heinlein and catapult rocks on Earth, that thing is dam big and easy to hit
Another Problem is Logistic and maintenance
is the Lunar site a full automatic Doomsday machine or manned Military outpost ?
the Doomsday machine is cheap, but we had to face the day if that dam thing goes berserk…
it's manned base you drive cost astronomic high, with resupply flights, who are also easy targets for enemy ABM...