> First, how do you even locate the carrier groups?
Perhaps by these SAR satellites China has been launching? SAR satellites have AFAIU been fairly effectively miniaturized recently, enabling a wannabe-superpower like China to send up hundreds or even thousands of them if they want to, making it infeasible to destroy them all cost-effectively at least with today's technology.
I'm not sure what the current level of coverage these things have, but it seems that today the technology exists to track surface naval assets day and night, and through clouds, at a somewhat affordable cost (for a superpower wannabe). So the trick of hiding a carrier battle group in the vast ocean might no longer work.
> the carrier group can move and also shoot down missiles.
Considerably more difficult for ballistic missiles. I would also imagine that missiles in principle could be relatively affordable if they were mass-produced; today they are expensive because they are expensive to develop and there's no demand for a huge number of them. So you could saturate the defenses with enough missiles that even if many were shot down, at some point a sufficient number of them are going to get through.
> Oh and once you do launch those missiles you’ve committed to a big time war, and you’re open to counter-attack by American forces - not just the carriers but also land-based strike forces.
Of course, but that goes the other way as well; if those carriers launch strikes against a big modern opponent you're also in for a big time war. I just hope neither side commits such a folly.
> It’s not like the United States is sitting around saying well jeez I guess China built these missiles and we can’t do anything.
Of course not. Then again, China probably doesn't build those missiles because they think US carrier groups will easily shoot them down. Both sides certainly have smart people, as well as ossified bureaucracies gunning for the last war.
Note I'm not saying the time of carriers is gone. But it's been 80 years since carriers became the kingmakers of naval force projection, and technology has developed quite a bit since, and there (luckily!) has been no major conflict testing out these new developments. I just think it's foolish to be very certain one way or another.