[ASA Vet]

the Battleship would be nearly invulnerable to anything other than a nuclear attack

You're correct. A Battleship would attract nukes.

[chuckwalla]

Then why don't carrier groups attract nukes?

[DarthVader]

"You're correct. A Battleship would attract nukes."

If a battleship or carrier got hit with nuke. I assure you that the capital city of the power that authorized such an attack would have mushroom clouds appear over it in short order.