Because they're the greatest peacetime weapons system ever invented. Until hot war breaks out, which seems increasingly unlikely under the umbrella of nuclear weapons and MAD, they are the premier force projection tool around--in essence, the best bluff a superpower can make, and crucially, it's worked since WW2.
That said, while incidents like Sweden "sinking" a carrier have happened and embarassed the Navy, carriers have been present in multiple wars since WW2 (Vietnam, Persian Gulf, Iraq War) and haven't been sunk. If it's really that easy, one would think it would have happened when enemies actually were motivated to inflict such a loss. This suggests that the wargame conditions aren't very reflective of actual doctrine.