Against the weapons that have actually been used an armored warship offers a real advantage.
Then why have new ships not been armoured for years?
Because the armor conveys an advantage in only the one narrow mission of shore bombardment. Prior to the 2000s the US always kept the BBs and some CAs in reserve for that role. The Russians kept the old Sverdlovs for the same purpose. You only need a couple of ships for that role, and they didn't need to be cutting edge so with cheap labor the old ships did the job just fine. As long as there were armored WW II ships in the mothball fleet there was no need to build new ones.
However now the US Navy faces a very different problem. Labor is now their main expense. Crewing the old BBs is simply too expensive, and the old 8" CAs are worn out and gone to the scrap yards. The original question of the thread was bring the BBs back or not. Because of the labor factor the answer has to be no. However that doesn't preclude the building of a new armored ship, it just probably will not look like a classic battleship.
It may not even have guns, as another poster pointed out an MLRS could do the job of providing a cheap, always available bombardment option. The cheap factor being important. Using million dollar a pop cruise missiles to blow up trucks is waging economic warfare on your own country. The US learned that lesson in Iraq and Afghanistan. They should have learned it in Vietnam, but that is another story.
And the armor does not need to be thick Krupp Steel plates. It might be composites, it could be Chobham. The mission defines the armor and a weight/cost/protection balance would need to be struck. As the old saying goes, good, cheap, light weight, pick two.
My point is that in the littorals you are likely to take hits. Probably not from the top end ship killing missiles of the big navies, but from artillery, suicide bombers, boats full of fanatics with RPGs or at worst a C-802 or silkworm somebody sold to a stateless operator. You want a ship that can take a hit from one of those and remain in action. Not survive without a scratch, but a least be able to depart under its own power.