Indeed, but that wasn't why they were built. They were built to be battleships, and their mission was to destroy enemy ships, particularly other battleships.
The Baltimore, Cleveland, and Atlanta/Oakland class cruisers all had impressive AA firepower as well. Except for the last, none of them were built to be AA ships. They were also more cost-effective as AA screen than the fast battleships and were significantly faster than the South Dakotas and North Carolinas.
I'm a big BB fan, of the Iowas in particular, but saying they were great because they were good AA ships is like saying USS Enterprise (CV6) was great because she was a good troop ship during Magic Carpet!
The Atlanta was a purpose built AA ship (and the two classes that followed as well). The Clevelands and Baltimores were gunships first, AA ships second.
However two recent books that I have just finished (Neptunes Inferno and Attack on Pearl Harbor) as well as James Dunnigans Victory at Sea make the very salient point that the big issue in the Pacific is tankers and oilers. Neither side had enough before 1944 for extended operations for both the carrier AND battleship fleets, so choices were made. The Japanese never had a enough (which is why they had to base in Brunei for much of 1944) and the principal reason that the entire Japanese battleline and the entire American battleline never showed up during the Solomons campaign was that shortage of oilers.
A battle between the old US BBs and the old Japanese BBs would have been interesting though if the tankers could have been found, and if Pearl Harbor had not been attempted by the Japanese we probably would have seen that duel... possibly in the Marshal Islands in 1943. The Japanese however planned for the Decisive Battle to be fought in the inner perimeter though, and built their fleet and logistics accordingly. Truk, their main base in the Pacific (outside of Taiwan and Japan itself) did not have enough fuel storage for their fleet, and depended on anchored tankers for fuel storage.
So mostly likely the big gunfight is in 1944, and it would have been the modern US BBs vs the Japanese battleline, and the Japanese battle line has severe disadvantages. The 4 Iowas can take the 2 Yamatos, while the 4 South Dakotas and 2 North Carolinas can easily take the 2 Nagatos (assuming the Mutsu doesn't have its fatal accident), 4 Kongos and the 4 older battleships. Especially when you throw in the massive American air power and by this point the numerical advantages in US cruisers vs Japanese cruisers.