A carrier is essentially a single large target that when taken out negates the effectiveness of your opponent. Not sure what its successor is. Probably some form of stealth ship (since that seems to be the focus) armed with smart missiles.
I heard the Chinese were playing around with torpedo/missile hybrids which apparently changed the game since they are apparently impossible/hard to stop. Its a fair assumption that the US has something similar (or is working on it).
The U.S. has treaty obligations requiring the ability to respond militarily to crises in Europe and Asia and so the requirement to be able to project power is basically enshrined in law. But most other countries want, at most, to be regional hegemons and so don't need a deep carrier capability.
So with that in mind it's still unclear what China plans to do exactly with their carrier. Presumably they will build some more, but they will never put it in combat against the USN (who have ample capability to destroy the carrier aircraft in the skies, and the carrier itself). But it's an awfully expensive fleet to maintain just to piss off Taiwan or Japan.
Plus the logistics pipeline to get fuel and food and such to all that hardware floating around in the ocean.
I have no idea what a carrier costs to operate, but for a normal mega-yacht, it's said to cost about 1/5th original purchase price per year. I'm guessing with the wear and tear on a Navy ship with aircraft banging around on it every few minutes it's something much higher.
What in the world do you mean by "modern warfighting"?
What they have is an incomplete project that's militarily useless for, at least, several more years, maybe a couple decades, if ever.
Also they might be waiting for UAV launches from nuclear subs. Might be cheaper and about as effective.
Perhaps building such ships would actually harm their international relations because it could be seen as a precursor to aggression.