A 16-inch Alaska would not replace Iowa's postwar prestige

Would a 16-inch-gun Alaska class make more sense to retain after the war than the Iowa class?

No; it would be a capable battlecruiser, but Iowa's battleship status made it the stronger answer to the prestige and deterrence problem posed by Kirov.

Rearming Alaska with six 16-inch guns would push the class from large cruiser toward battlecruiser status. That stronger ship could have useful wartime and postwar capability. It would not carry the institutional and public prestige of the Iowa class, however. Kirov's appearance created enough anxiety for British debate over the earlier disposal of Vanguard, showing how symbolic equivalence mattered. Reactivated Iowas therefore offered a political as well as military answer that a modified Alaska could not fully provide.