I am not following military might of nations for some time. But not so long ago, even US strikers were no match for Russian equivalents for raw speed and range. US strikers scored on maneuverability, useful in dog fights. In a ballistic missile vs striker battle, maneuverability may allow US strikers to dodge a missile or two but if several are fired at the same time, it will be difficult to dodge all.
USN dun believe in dogfight since WW2. USN fighters was not design to dogfight, in fact, USN aviators were taught to dive and shoot and run away. USN fighters cannot outurn zeke but can outdive zeke so tactic was to dive in to attack jap aircraft and then climb to do all over again.
then missiles came along and USN believe in outshooting the opposition which was why AIM54 phoenix was develop for the F14 tomcat which have the range of over 100 miles at mach 5. fire all 6 at max range then turn escape enemy missiles. The US aviators are not as good as Top Gun suggest but a big part count the on the help given by the E2C hawkeye to outsmart the enemy. without the E2C, the capabilities of the USN aviators reduce by a lot. without the E2C, the "bubble" containing the CBG would be considerably smaller and give the CBG less reaction time out countermeasure in the event of an enemy attack.
As for balllistic missiles, it was claimed that the Aegis system can shoot down ballistic missiles but each ship had only either a 96 or 122 shot magazine depending on the ship class. so if PRC can one time target the CBG with 500 ballistic missiles confirm can overwhelm the CBG defense system.