Even if there are enough nuclear bombs to hit every population center, there's no guarantee they'll be fired. They might get destroyed before they can be deployed (easier with submarines and aircraft), never get launch orders, be held in reserve for future use (the Russians might have concerns about China, frex), or might not even be slated for use at all.
(I remember a claim once that the reason there were so many bombs was inter-service rivalry--if one branch had X number of bombs, another branch would want the same number, etc. I assume people would not be launching nukes just to launch them.)
Also population centers need more bombs for each. Even a bomb the size of the Czar Bomb would only directly destroy the very center of what we consider Metropolitan New York City. Of course that would mean a huge number of casualties, and more importantly it would create fires for many miles around that would burn for weeks, if not months, on end. But even hitting every population center say, three times, would still leave people on the outskirts that could fairly easily survive the fallout provided they had enough provisions for a week or so.