Part of it is style. They LOOK like fighting ships. They LOOK impressive. When you see those big guns, there's absolutely no question in anyone's mind what they can do. That's actually important for "showing the flag".
But there's substance too. In the real world, battleships have repeatedly proven themselves, despite their critics. (The critics have been around at least since the beginning of the Dreadnaught era, c. 1906, and probably a lot longer.) The battleships was of course THE capital warship during World War I, though US battleships played only a minor part in that war. In WW II, after Pearl Harbor, on those occasions American battleships were actually given a chance to fight they did quite well. Notable actions include the Naval Battle of Guadalcanal, the Battle of the Santa Cruz Islands, the Battle of Casablanca, and of course, the Battle of Surigao Strait. Battleships were also extensively used for shore bombardment in support of amphibious assaults, which is one reason no US amphibious landing was ever repulsed. After WW II, almost all of the battleships were retired as obsolete, until the Missouri proved herself a valuable shore bombardment ship in Korea. Her sisters then came out of retirement, and did just as well. The New Jersey came out of retirement again in 1968 for Viet Nam, and again proved her value as a gunfire support ship; in fact she was so effective that North Vietnamese negotiators threatened to suspend peace talks unless she was withdrawn! All four remaining Iowa-class battleships were reactivated in the 1980s. The New Jersey provided critical gunfire support in Lebanon in 1983. The Missouri and especially the Wisconsin did the same in the Gulf War of 1991. Despite their utility, they were all retired again, and they will not really be replaced. The heavy fire support capability they provided is effectively gone forever.
We're both involved with the campaign to save the Battleship New Jersey.
For more information about battleships, try The Wells Brothers' Battleship Index.