Sure. But if the carrier group is "projecting power" in the middle of the ocean, who cares? Get close enough to shore so it can project its power over some militarily interesting area, and it starts to get in range of all kinds of scary weaponry. Assuming a technologically advanced adversary, and not a bunch of goons with Ak-47's and RPG's, of course.

So in the end I guess the question is whether a carrier group is a cost-effective power projection tool in the age of supersonic (or even ballistic, if we choose to believe those Chinese things are real) anti-ship missiles, submarines and whatnot. Or are they just like battleships in WWII?