The Iowas are far too short between decks. They were built in a time when a tall man was 5'8" (my grandpa was 5'4" and average for his age), and now the entire upper third of a boot camp cycle is over 6' tall.
Plus, you do NOT want to know how much it'd cost to refit a nuc plant into the Iowas. (Give you a hint: about as much as building a new carrier)
Not to mention that the US can't make new ammo for the big guns, let alone new gun tubes. I think 8"/203mm is as big as we can make, and I'm not sure about that!
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If I was going to build an armored ship to go sail in harm's way, in an intense A2AD environment, I'd build something along the lines of a Worchester (680ft long, 12x6" guns in 6x turrets) or a Des Moines (716ft long, 9x8" guns in 3x turrets). Maybe as big as an Alaska (808ft long, 9x12" guns in 3x turrets), but that would need a clean-sheet design, the Alaskas were lacking in underwater protection.
I would only use nuclear power if we were installing a bigass antimissile laser (or two), it's much easier to run gas turbines. Nuclear power is designed for each class specifically, there's not a whole lot of cross-compatibility between classes. Even for submarines.
A Free-electron laser that puts 100megawatts on target needs 165MW electrical power input (and has to dissipate 65MW of waste heat!) That's an entire nuclear plant all by itself, so you'd need a second plant to run the ship. Why so big? Because unclassified SDI testing in the 1980s showed that you needed to dump 25MW of energy onto a missile to kill it. It took the 5MW laser 5 seconds to kill a TOW missile, it took that same laser 5 seconds to kill a Titan missile. You need a laser that can deliver the required energy in a fraction of a second in order to deal with Soviet/Chinese-sized missile swarms. At 100MW beam energy, you can kill 2-3 missiles a second, in 0.25sec pulses.
Hull wise, only the Alaska-class CBs had more than 8" of armor, but again, they were lacking in underwater protection and modern torpedoes are much nastier than WW2 torps. So it'd take a lot of re-designing to make them better.
I'd probably build a Des Moines, replace the 8" guns with railguns, the centerline 5"/38 guns with 5"/62s (the same guns as on modern ships), the flank 3" guns with VLS, but the bow and stern 3" guns get replaced with 57mm Bofors. The flank 5" guns would get replaced with CIWS mounts (because the only better spots are taken by the gun directors for the main battery!) A possible modification would be to remove the after turret and install a helo hangar, instead of having any helo(s) always exposed on the fantail. An alternative would be to cut down the fantail like on the Burke-class DDGs and re-locate the stern 57mm guns to the top of the hangar. This might require raising the after turrets, however.