The Iowa vs Yamato almost happened.
Nimitz initially just sent his 6 battleships to intercept Yamato at Okinawa, to let them shoot it out.
Rear Adm Dayo, however, in charge of the carriers, steamed North on his own initiative and when he was in range cabled Nimitz that he was ready and asking for permission to attack.
Nimitz's reply: "You go get them."
Obviously, Yamato would have been sunk anyways, but of course Nimitz made the right call - 10 pilots lost against the possibility of losing several thousand lives if Yamato managed to score a couple of lucky hits on the American battleships' magazines.
Yes, Yamato might have scored some hits before the 16" guns of the USN got it in range. At that point, however, not only given the USN's numerical superiority, but given the radar ranging capabilities of the US battleships, Yamato would have been annihilated. (Remember what happened to battleships Fuso and Yamashiro at Surigao Strait in the middle of the night in Oct 1944. The accuracy of the USN battleship fire was nothing short of incredible.)
You also have to remember that the 16" guns of the USN had a faster rate of fire that the Yamato's 18" guns which took something like (I can't remember exactly) somewhere between 1/2 minute and 1 1/2 minutes longer to load for the next salvo.
In a one-on-one between Iowa and Yamato, it would have been a much closer run thing. Yamato's greater punch and range versus Iowa's faster rate of fire and radar ranging. Yamato's optical range finders proved their worth at Samar - the indisputable film evidence of Yamato's 18" rounds bracketing - and finally impacting - White Plains at 33,000 yards is a pretty amazing testimony to the superiority of Yamato's optics over anything similar that any of the other powers had at that time. One of the Futabayasha books has a CGI recreation of what the actual optical range finding control center looked like, and it is truly amazing - something like out of one of the Star Wars films. If I have a chance I'll try to find it scan it and post it.
I'd love to have the opinions of some folks who are actually familiar with the technology involved in this type of optical targeting ....