Maybe, just maybe, the author should have studied a littel bit of one of thr most powerful navies of the early 20th century, the Imperial Japanese one. Because they liked their battleships a lot, despite prioneering modern naval aviation and despite never using their battleships in direct combat.
But the point of a battleship wasn't just showing off, it was also area denial. You really can't move another surface combatant into an area with a battleship unless it is a battleship (that didn't stop Taffy 3 [3] from trying). So battleships served two clear roles IMO: Area denial and shore bombardment. There is a reason the US Navy kept the Iowas around until the 90s. For what they do there is nothing like them. That said let's also be clear the counter to a battleship is an aircraft carrier, not a battleship based on existing data.
[1] https://en.wikipedia.org/wiki/Battle_of_Leyte_Gulf#Battle_of... [2] https://en.wikipedia.org/wiki/Naval_Battle_of_Guadalcanal [3] https://en.wikipedia.org/wiki/Battle_off_Samar
Another thing the article misses: submarines were rendered useless by ASW tactics and technology by end of '43. It took the first true submarines in late '44 and '45 to change that again.
And a design, battleships, that stayed between the very early 1900s until the 90s in various forms and shapes proved its usefulness.