I am not certain that Aegis can defeat a DF-21. Aegis could be effective against tactical ballistic missiles, but the DF-21 is a long range device that would overfly Aegis’ radar fence. Taiwan is installing long range surveillance radar, equivalent to PAVE PAWS, to keep an eye on China, which would almost certainly detect the launch of a DF21, if not effectively jammed.
What really, truly puzzles me is how they think you can get 200 kT from a FAE with a payload much less than one ton?
I also wonder about the OTH radar part. In time of hostilites, nothing would be easier to jam or spoof than an OTH radar. If they are going to track the carriers by satellite, they better pray for clear skies.
Current Aegis class ships with SM3s have anti-ballistic missile capabilities. I think the DF-21 would be a piece of cake.