I feel that three criteria define any ship: its size, its defenses , and its role, which for battleships were large, armored, strike and antisurface respectively
by the definitions above I still feel the SSGNs are today's best examples of the good ol' battleships as they are large, have the stealth only a submarine can provide as its defense, and have an immense strike capability. Surely, they are submarines and not surface ships, but again I feel that is more a credit to stealth as a defense instead of being a giant armored target for missles, bombs, torpedoes or what have you that battleships would be in today's threat environment. Look at the Kirovs, arguably the best example of a modern battleship in service. They're big and expensive to operate and require escorts further adding to their cost
OTOH we have the Zumwalts which are certainly large surface combatants with an emphasis on land attack, but they strike me as too similar to the Kirov's in that they're large expensive surface combatants that are either too vulnerable on their own or too costly to operate if deployed with escorts.
In closing, battleships in and of themselves would be too expensive to operate, its roles are done better or more efficiently by other assets, and too vulnerable. Three strikes and they're out!