Good question but we can say with certainty that the Chinese are extensively practicing and improving/refining their ability t do so with the aid of various ISR assets.
As there's zero transparency with the Chinese military we simply do not know how realistic any of their tests are. Do we even have reason to believe they would have staged a realistic test?
Stop and think about what a realistic test is. That would have required a target ship that could decide where it wanted to move, was capable of changing its speed and could move at least at the speed of a
conventional warship USN frigate, even if we assume it wasn't going to move at the speed of a nuclear-powered carrier or AB destroyer. It would also require Chinese assets being able to locate the target in a certain timeframe to simulate the danger of them (the tracking assets) being attacked.
I have litte reason to think that they have not hit moving targets. However, it would have been a lot easier to hit a target moving at the speed of a commerical ship - let's say 18 knots - that was on a fixed course, where it was known where the vessel was and where it was likely to be when the missile hit it. And, of course, with no attempts to intercept the missile or attack tracking aircraft.
China will try to improve their missiles, but they are not going to for one minute admit that they currently would be unlikely to hit a carrier, or indeed that they would struggle to make one that will ever be likely to do that. The propaganda and fear factor is simply too valuable for them, both domestically and internationally. USN carriers are a key part of the fleet, if they can sow the seeds of doubt into the minds of the American government about the safety of those carriers they may be able to deter the US intervening if or when China attacks one of its neighbours.
None of this means the threat should be dismissed, and it is sensible to keep working on anti ballistic missile defences for the surface fleet. However, I think there are some people who are, whether they realise it or not, simply accepting Chinese propaganda at face value that they have or will have an effective counter to carriers. Whether that's out of awe and/or fear, that's not logical.
You One must look at how realistic any of the tests staged could be, as well as look at countermeasures like the SM-6.
Don't forget, we've been here before. When the PLAN acquired Sovremennys with Sunburns and Kilo-class submarines with Clubs, there were people in full headless-chicken-mode saying that the carriers were now going to be useless to fight a war with China. What happened? The USN just ensured it improved its defences.
If
you we don't look at this logically,
you're it's inviting defeatism and would give China exactly what it wants, a militarily compliant US without having to fire a single shot.
They'll be operating on their home turf; are motivated and will be well acquaint with their equipment.
This isn't a land war in China, nor is this the 16th century in the English Channel where knowing the weather, location of sandbanks, etc is vital. The PLA remains a military whose most recent "combat" experience is massacring civilians (and pushing foreign unarmed soldiers down ravines).
More importantly, don't think for a minute that USN surface vessels are going to be operating within range of Chinese land based AShM batteries, at least in the inital stages of the conflict. I would assume that the surface fleet is initially mostly going to be standing back to the East, North and perhaps South of Taiwan, creating safe corridors for supplies and guarding the carriers. It's only the submarines that would be getting nearer to China.
