Technology is an endless game of cat and mouse. But... If you imagine a carrier battle group and you ask "is there a way to create a missile defence system so that the carrier is protected?" The answer is yes, but every few years we will have an 'oh shit' moment where the other side comes up with something new and we have to counter it in a hurry. However, you keep a few extra carriers in your back pocket and we should be able to protect them from a strategic perspective.

However, can you do that without losing some support ships? No.

When it comes to nuclear war you can't just say it is ok if Washington survives. A single major US city getting nuked is totally unacceptable and it is hard to imagine any foreign policy situation that would justify that happening in exchange for some "win" abroad.

What missile defence is about is out-spending the little guys. North Korea, Iran, (hell even Russia), could easily find themselves in a situation where they simply cannot afford to keep playing the game to have nuclear arsenals that represent a credible threat to the USA. China's different. So even though the system could be defeated, you can make it cost trillions of dollars to be able to do so.