After both sides had nuclear weapons, a conventional war was not only unlikely, but would prove fruitless. 1,000 tanks couldn't accomplish what a single bomber carrying nuclear weapons could.

A full scale invasion of Russia had proven impossible, and it is widely agreed an invasion of the United States is unfathomably difficult. This leaves the European theater with its smaller nations, but military concentration remained high enough (no chance of a devastating opening salvo) for long enough for both sides to develop capabilities of rapid and widespread nuclear strikes. Western Europe was out of the question soon after WWII, which is why conventional conflict manifested itself only in the wars in Southeast Asia. These containment wars were small enough that replenishment wasn't a huge concern.

If war broke out after nuclear armament, there wouldn't be enough time, or even the need for nations to spool their industrial manufacturing up to wartime speeds. It wouldn't last that long.