The only time I can recall a nuclear weapon being used in the Third Succession War was during the Draconis Combine invasion of Skye where a 1.5 kiloton nuclear demolition charge was used to blow up a dam to halt a Draconis Combine attack on the city of New Iverness.
But given the number of nuclear and other weapons thrown around during the First & Second Succcession Wars it seems to me rather odd that EVERY combatant in the Inner Sphere would suddenly start saying "we not going nuclear anymore"
At the very least, it seems that decades of horrible atrocities and destruction would leave enough raw hatred that there would still be an inclination to get "pay back" on a nuclear scale now and then.