Sorry, but no.
I won't talk about infantries and land warfare in general since it's not my field of expertise and focus, but your attempts at shoehorning your reasonings across domains which shouldn't be seen as equivalents is just hilarious.
Surface warships are very much a must for not just fighting naval wars against the enemy, but also for establishing presence and control at sea. You can't do that with missiles for the latter.
Surface warships of today mainly rely on active defensive measures, namely radars and sensor systems, anti-air and anti-missile interceptor missiles, gun-based or DEW-based CIWS, electronic warfare/countermeasures (jamming, spoofing), decoys (smokescreen, towed decoys), and stealth (for certain ships) for defenses against enemy warplanes and missiles.
And as a matter of fact - Shields and swords are always engaged in a never-ending arms race, and this has been true ever since the first humans graduated from the apes. You don't see the enemy putting up their arms and say "I yield! You win!" whenever the opposing side develops some new technology to overwhelm the enemy - They always adapt and develop something better to defend and overcome against whatever new technology the opposing side fields. The cycle continues indefinitely, because survival is the fundamental instinct of the human race.
Moreover, you've been looking at things rather simplistically. Anti-missile defenses don't just rely on ships themselves - It's an all-encompassing effort across multiple domains: Primarily land, sea and air, but now with the addition of outer space, cyberspace and information space as well.
If anything - I'd say that aircraft carriers are actually becoming more important than ever before, not just as additional means of offense (i.e. delivering strikes against enemy warships and land targets), but also additional means of defense (i.e. ship and fleet defenses against increasingly advanced and lethal anti-ship missiles).
