Nuclear deterrence has limits that do not allow you to neglect conventional military power:
In short, nukes can deter some things — but not the things allies fret about on a day-to-day basis. It’s doubtful U.S. leaders would pull the nuclear trigger over, say, the Senkaku Islands or China’s nine-dashed line in the South China Sea. It takes conventional armies, navies, and air forces to manage such controversies. Yet Asian allies see vital interests at stake in such struggles, even if Americans don’t. If the allies lose faith in U.S. military might, and conclude they cannot field forces strong enough to ward off Russia or China, then they may seek nuclear deterrents of their own. The kaleidoscope turns.
Ergo, if U.S. leaders want to simplify the geometry of deterrence — and keep Asia from descending into brutish, Hobbesian competition of all against all — then they must keep the number of nuclear-weapon states as compact as possible. By sustaining a credible nuclear deterrent in concert with unbeatable conventional forces, Washington can suppress U.S. allies’ incentive to burst through the nuclear barrier. Again: nuclear strategy is indivisible from strategy.
And a bonus for discussing how others' rational is not necessarily our rational. I touched on both aspects recently.