There is a lot of speculation... Since the Navy has spent so much on these things ... I'm fairly certain that classified counter measures are either deployed or coming ... most likely already deployed.
If the aircraft carrier is outdated it is strange that the Chinese have been and continue to pour huge sums into trying to build carriers..
You have FAR too much faith in our military and leaders.
Russia has had these missiles (some of which are hypersonic) for a while, our best defense is to literally make a
wall of explosive bullets using the CWIS. It works but it's not perfect and can be inundated pretty easily. We're also working on a laser defense system as well as electronic counter measures. It only takes one of these to take out a carrier and at the speed they travel there's little time to do much (I question a laser being capable any time soon).
As for carriers themselves, let me explain a bit of military history for you...
In 1921 General Billy Mitchell said he could take out a Battleship with bombers, they laughed and demoted him. Seven years later he managed to do a demonstration where even with the odds stacked against him he proved his point. They claimed he cheated then tried to fire him, public outcry saved him. 25 years later the Japanese attacked and our battleship fleet was in ruins. Carriers became capital ships by default, not by choice of the Navy.
That remains today.
Reagan wanted to bring back the Battleship. Our current Senate has recently considered bringing them back and even Trump has said as much. And no, they don't mean build new ones, they actually want to bring the old Iowa class out of mothballs even before we start building new ones. It's not militarily advantageous to bring them back, it's simply political. "Look at what we have!" Why keep our carriers? Because at least they're more usefull than battleships. Seriously, that's really about the best reason, we don't need them, just like we really don't need bombers,* but they too are a political tool.
The government and military loves their toys, the bigger and more of them the better.
They don't care the reasons or justifications, the fact that they can have a carrier is the only reason they need to have a carrier. Do we NEED 11 carriers, of course not, but WE CAN so we do.
Why are the Chinese building one?
There's two primary reasons to have a carrier, political and force extension. Carriers are a symbol of world power, something China desperately wants to show. As for force extension, we have airstrips the world over and long range aircraft, two things China still greatly lacks. Their only option to extend the range of their forces is with a carrier.
*We have cruise missiles. Cruise missiles are a bit over $1mil per missile. Not cheap. However, consider the manpower, fuel, training, etc. behind a ship or bomber to put bombs on target, suddenly it's really not far off even for a cheap bomb and if you lose just a single ship or aircraft the odds greatly tip in favor of the cruise missile. B2. "But Battleships use guns and bullets are cheap!" One problem with bringing back battleships was gun range, they solved this with a 130mile range rail gun, sounds great except 130 miles isn't far enough and worse, each round cost more than a cruise missile, which is more accurate and can be fired from land, air or a smaller ship. All of which is precisely why cruise missiles have been favored by the last few Presidents for retaliation, even when a carrier is sitting right off the coast.
