As @Capn_Carl said, the OP specified a similar attack to that of the Yamato, which would not be realistic, but it is still an interesting question. Of course, in real life, battleships didn’t adventure out by themselves in the Pacific because they were vulnerable, but it’s interesting to compare the two ships and see how an Iowa class BB would have fared.
I was responding to @Limmin because they believe that Japanese would have succeeded against Iowa even with CAP and I disagree with that, especially in the later stage of the war. Air cover would have protected her.
In a WWII History Roundtable presentation, Jon Parshall, co-author of Shattered Sword discusses the prior history, and logic leading to Japan’s development of kamikaze forces during World War II, and talks about the tremendous increase in AA firepower. This is a bit of the presentation, starting here.
Later in the war, Task Force 38/58 would be about 120 vessels with 1,200 to 1,500 aircraft and an increasing bias towards fighters. There would be 952 5” barrels, 3,136 40 mm barrels, 2,926 20 mm barrels.
As the war continued, the trend was towards increasing size, weight cyclic rate and overall firepower of AA weapons. The CAP was controlled centrally within the combat information center.
In 1942, the CAP had a radius of 25 miles, 1944, it was 60 miles.
The 5” and the 40 mm guns were the best in the war, being directed by the Mk 37 director, the best of the directors in the war.
At the battle of Midway, a typical carrier formation of a CV, two CA and four DD would put up about 32,000 lbs / min in AA explosives and steel. This is about two or three times as much as the Japanese formation.
In late 1944, with a CV, one BB, one CA, one CLAA and three DD, then it would be 162,000 lbs/min.
The BB in 1944 had more than firepower than the entire formation in June, ’42.
Factoring in the effect of the VT fuze, the effective weight was 575,000 lbs/min about an 11,000 times increase so it was suicidal to even approach a task force. This was the reasoning behind the formation of kamakaze in that if they were going to lose their lives, they might as well have a meaning for it.
After the invasion of Okinawa, the IJA and IJN sent joint tokko missions, called Kikusui. The first mission, Kikusui 1 had 230 IJN planes and 125 IJA planes for a total of 355 tokko attackers.
Obviously, an American battleship safely within a task force simply would not be vulnerable, but that’s a boring answer. On its own with a few other ships against a hypothetical US enemy, it would be sunk.