US generals are not idiots, they're not going to sail their Carrier Strike Groups (CSGs) straight into a hailstorm of Anti Ship Ballistic Missiles (ASBMs) equipped with either Maneuverable Re-entry Vehicles (MaRVs) or Hypersonic Glide Vehicles (HGVs) as warheads. The Chinese DF-17 HGV equipped ASBM, and the DF-21D MaRV equipped ASBM, have a range of around 1600km/1000mi. The DF-21 is said to be a Chinese equivalent to the now retired Pershing-II from the United States. So these weapons will act as area denial weapons, with the CSGs remaining outside of their effective range during the majority of their operations. Aircraft will rely on mid air refueling and/or external drop tanks to have the required range to conduct missions from this far out. This of course restricts their operations, but they can still carry out missions. This is also why there's a huge focus on increasing the internal fuel capacity and range for the US Navy's 6th generation strike fighter (F/A-XX), and why the F-35C has such a large internal fuel capacity.

Pershing-II (left), hypothesised DF-21D MaRV on top of DF-15 booster stage (centre), DF-21 with nosecone shield (right):

DF-17 with DF-ZF HGV:

We can see this in Yemen in the Red Sea (where ASBMs were used as weapons for the first time in history), where the USS Harry Truman aircraft carrier spends the majority of time around Jeddah, around 700-800km away from the Houthi/Ansarallah controlled parts of Yemen, and resupplies at Yanbu. This keeps them out of range of the Zulfiqar Basir MaRV equipped ASBM (700km range) during normal operations, and keeps them out of range of Anti Ship Cruise Missiles like the Abu Mhadi (1000km range) when resupplying.

Zulfiqar Basir, with a close up on the electro optical sensor on the MaRV for terminal guidance:

Area denial is still a great capability to have, but ASBMs aren't magic wands that can just eliminate CSGs. They have their own limitations, hitting a moving target such as a ship with a ballistic missile, even one equipped with a HGV or MaRV, is quite complex, especially at longer ranges where you'd have to provide midcourse guidance updates and resulting trajectory changes to a ballistic missile in space. This is why longer range ASBMs aren't there yet. To try extend the effective range of existing ASBM platforms, they could be launched from aircraft, which give a small range boost from the launch point, and allowing the aircraft to fly out over sea before launching, for a combined range extension (aircrafts range + ASBM range). China does have the KF-21, an air launched DF-21. The challenge then becomes avoiding the launch aircraft being intercepted by hostile combat air patrols before launching, such patrols will limit how far out the launch aircraft can fly.

Air launched DF-21 variant mounted on a Xian H-6, the two solid fueled booster rocket stages and MaRV are clearly visible.

The article mentions equipping a longer range ballistic missile like the DF-27 with a DF-ZF HGV, but I don't think that's practical over the ranges mentioned (8000km/5000mi). The DF-ZF is not designed to glide at hypersonic speeds for such a long distance, so your glide phase would take up a small part of the overall flight profile, meaning that such a platform would act like a conventional ballistic missile for the majority of it's flight time. The DF-ZF is also not designed to handle atmospheric re-entry at the higher speeds and loads that such an extended range would require. A new HGV would be needed.