AFAIK, there is no historical instance of naval bombardment by a battleship wiping out a land unit. So lethal bombard would really not be appropriate. Battleships are made to sink other ships, though they have provided valuable gunfire support inland on many occasions.
I think the battleship need to be treated solely as an Industrial Age naval superiority unit. Going up against Industrial Age cruisers, destroyers, and everything earlier, it should be able to win the day most times. I would disregard the upgrading of WWII battleships with better AA and cruise missiles, as the player shouldn't be getting this kind of performance from an older unit for so long. (upgrade, upgrade

)
Going up against naval air changes the equation drastically. The only way a battleship should ever get to a carrier is if it catches it all alone. Stacking a destroyer or cruiser with a carrier would guarantee warning of attack, and all the carrier planes could strafe the carrier before it moves in for a melee attack, and then it must engage the cruiser/destroyer screen before closing on the carrier itself, which makes success unlikely. Same thing should apply with subs - destroyers in the carrier group will actively engage the subs before they can close with the carrier. So, you would need a lot of battleships or subs to get in there and nail the carrier itself, especially if some kind of force multiplier bonus is applied.
A modern carrier group with a nuclear carrier and jet fighters should receive combat bonuses so strong as to render an assault by any industrial age naval unit tatamount to suicide. A modern carrier group should also be able to see several tiles around it. AEGIS cruisers and modern destroyers/frigates would provide the same sort of screening in modern times against attack by either land or naval aircraft and fast attack subs.