Which U.S. 16" gun? The 16/45 would add roughly 40 tons of topside weight and the 16/50 would add better than 200 tons. I would guess, depending on the rest of the refit, that the 16/50 would make the ship extremely top heavy, to the point that the ship would be a hazard.
The 16/45 added weight would be more manageable, but even then the weight that, IOTL, was dedicated to additional AAA would have to be left off. With the demonstrated weakness in the KGV class original AAA layout that would not be a wise decision.
There is also the not inconsiderable difference in shell weight. The 14/45 Mk VII on the KGV used a 1590 pound shell (both the AP & HE rounds were this weight). All the handling equipment on the ship was designed to work with shells in that weight range. The U.S. 16/45 & 16/50 used a 1,900 pound HE and a 2,700 pound AP shell. Could the KGV shell handling equipment manage a 60% heavier shell? For that matter the 16" U.S. shell was a foot longer than the RN shell, what does that do to the magazine storage and shell handling. These shell sizes are considerably larger than even the shells of the proposed 15" guns that were under consideration for the KGV class )and the USN AP round is 35% heavier than even the 16" shell used on the Nelson class)
Lastly these is the issue of speed. The KGV were not exactly speedboats to begin with at 28 knots. They can't give up too much speed before they start to hold back the carriers, and the addition of the sort of weight and other changes you are discussing here will cost them several knots. This is one of those things that keeps on giving since a 25 knot ship may be right on the edge of being able to do the job but the same ship with a fouled bottom (aka the normal state of a ship) is probably now at 21-22.5 knots.
The reality is that battleships are built around their guns. Trying to "up-gun" one is a practical impossibility. Up-gunning is hard to do with a tank, with a warship it is nigh on impossible.
