A nuclear warhead on a D21d aimed at a carrier would be utterly pointless. If you want to deliver a nuclear warhead against a carrier task group, a supersonic antiship cruise missile would be a far, far cheaper and more reliable method to do so. The Chinese have the P-270 Moskit (NATO: SS-N-21 Sunburn), which would be well suited for such a task. To waste an extremely valuable and scarce resource like a ballistic missile on something that could be better done by a relatively inexpensive antiship missile would be silly. And there is also the small point that the Chinese know full well that if they nuked an American carrier we would incinerate their entire nation.
No, the idea is that the conventional warhead D21d is supposed to be more difficult to defend against than anti-shp cruise missiles. It is, but whether it is good enough to get past our Aegis system remains to be seen. I very much doubt it. The D21d reentry vehicle must slow after reentry to allow enough maneuver time to course correct and have a chance of actually hitting its target. If it has a passive infrared targeting sensor, it would also have to shed its heat shield nosecone to expose the optical sensor. If it is RADAR guided, it will essentially be emitting a targeting beacon for our anti-ballistic missiles to home in on. The RV will be coming down at supersonic, but not hypersonic speeds, so it should not be any more difficult a target than a regular tactical ballistic missile, and we already know that Aegis works quite well on those.