Well currently, a ship of your specifications is not feasible because it may suffer from survival issues due to its extremely large electromagnetic signature, physical/radar signature which renders it vulnerable to advanced supersonic anti ship missiles such as the Russian Yakhont, Indian Brahmos, US RATTLERS, Taiwanese Hsiung Feng-III etc. which all have evasive flight patterns and advanced seeker heads that will easily lock on to a ship of battleship size (greater than 50,000 tons displacement) and put it out of action or sink it. Anti Submarine warfare will also be a no-no for the battleship as the wake turbulence generated by such a ship will make ASW warfare almost impossible without ASW helicopters or planes-unless the battleship is accompanied by escorts.
However, new air defense technology such as the "laser phalanx" that is said to be extremely effective vs cruise missiles/antiship missiles and may well prove such a concept feasible and in the future a ship like this may be built if funding permits and if it is suitable for naval requirements-although not reaching the size of a supercarrier for sure.
Such a "battleship" will be the best type of ship available for naval support for the Marines when they hit the beach as well as being able to engage enemy ships with guns (new Excalibur projectile allows pinpoint strikes) and super/hyper sonic antiship missiles. Air defence for a Nimitz Class ship is a serious issue which being unable to launch fleet defense interceptors of its own, the battleship is at a serious disadvantage-explaining why the USN has opted to build more supercarriers.
The Kirov class cruiser wasn't such a bad idea for its time, but in the present age, has serious survivalbility issues as it cannot withstand more than one Mk48 ADCAP strikes or supersonic AShM hits.