Even without nuclear weapons, I've got to think that countermeasures are easily overwhelmed, and the cost of a few dozen long-range anti-carrier missiles must be negligible compared to the advantage of incapacitating a carrier (at least for a top-tier adversary like China or Russia), right?

I'm not sure. Throwing a few dozen missiles from long range against a carrier group, complete with airplanes, may not work very well. They'll have a few dozen fighters, multiple Phalanx guns, shipboard missiles, and a lot of electronic counter-attacks. I think they will only be "easily" overwhelmed if they've got an attack method that is hard for the carrier group to counterattack. That is harder than it looks.

I have no idea and I hope you're right, but airplanes and missiles aren't implicitly anti ballistic countermeasures. Certainly there are some anti ballistic missiles and fighters which are equipped with anti-ballistic tech, but I don't have any idea how effective they'd be in a barrage scenario.