I remember, when I visited the USS Iowa in Los Angeles, they gave us the dimensions of the ship and mentioned that the class was designed specifically to be able to fit through the Panama Canal, as being able to quickly move naval vessels from coast to coast was naturally very important to the US Navy and government.
But today's supercarriers like the Nimitz class are obviously way too big to fit through the canal; at what point did the USN decide that, for at least some of their ships, fitting through the canal was less important than the other operational abilities gained by large size? Was it a contentious decision, or simply bowing to the increasing size of new technology and new aircraft? Did the Navy consider making anything other than aircraft carriers too big to fit?
For those unfamiliar, when OP says that the Iowas were designed specifically to fit through the Panama Canal, he's not joking. They had about a foot to spare on either side when they went through the canal.
To my knowledge, the first ships the US Navy ordered that wouldn't fit through the Panama Canal were the Montana-class battleships authorized by Congress with the 1940 Vinson-Walsh Act (often called the Two-Ocean Navy Act) which was the largest of the bills that expanded the size of the Navy before the war began. The Vinson-Walsh Act authorized the final two Iowa-class battleships that were never completed, Illinois and Kentucky, as well as five Montana-class battleships.
The design of the Montanas shared some similarities to the Iowas, but they were intended to be even bigger, mount a fourth main turret, and carry heavier armor. They would have been slower than the Iowas, but with a top speed of 28 knots were still planned to be faster than what were considered "slow" battleships of the time. Construction actually began on some of the Montanas but was halted in late May 1942, as it became apparent that shipyard capacity was needed to build other ships. The Montanas were canceled in 1943 and were broken up without making it off the slipway.
The first American warship that was actually too large to transit the canal was USS Midway, an aircraft carrier design that was laid down in 1943 but not finished until September 1945, just a few days after the Japanese formally signed the Instrument of Surrender in Tokyo Bay. American aircraft design, as I've mentioned before, had to comply with the pre-war naval treaties that limited the size and number of aircraft carriers that could be built. That required tradeoffs, such as the American choice to carry larger air wings and forego an armored flight deck. The Midway class didn't need to make those sacrifices. It was the first American carrier with an armored flight deck, and did so while carrying more aircraft than its predecessors. You could consider the Midway class to be a bridge between the Essex-class carriers that were the backbone of the US fleet in World War II and the supercarriers that came later with the Forrestal class. As is still the case, lessons learned from older designs influenced newer designs.
Midway herself served until the early 1990s and even participated in Desert Storm, though she underwent many changes over the years. If you've seen Iowa in Los Angeles, you may be able to take a day trip and visit Midway in San Diego. You can read some information on her construction here and here, though there's nothing too technical.
Someone else may have more information than I do, but I don't think the decision to build the Midway class was particularly contentious. The choice was made during the war as American shipyards were cranking out new hulls at rates never matched before or since. The decision was not that the US would be building new aircraft carriers that were too big to go through the Panama Canal instead of smaller ones, because they were building plenty of carriers that could transit the canal also.
Edit: While reading a bit more, I've learned that 3 older battleships that were rebuilt after Pearl Harbor (Tennessee, West Virginia, California) became too large to transit the canal also. These ships were ready before Midway, but it seems like that's not what OP is asking.
The United States signed the Destroyers for Bases agreement with the United Kingdom in 1940.
After the fall of France in late June 1940, it was looking increasingly likely that Britain would surrender without help from the US. Roosevelt was constrained by the upcoming election from appearing too pro war, but it was decided that the US needed to send some kind of support to Britain.
The United States wanted to be able to build airfields in newfoundland, Bermuda and Trinidad. Churchill said, not without something in return, so Roosevelt send 50 old destoyers to help. In exchange they recieved 99 year leases to build naval or air bases on British posessions in the Carribean and Newfoundland.
The end of pre war naval agreements restricting the size of ship building industry, and the size of ships ended. So they started to build more, and build faster. With their new posessions they could also build new bases, giving the United States for the first time the ability to have more than one fleet.
It was no longer really necessary to plan on transiting your fleets from one theatre to another - though after the decimation of the Pacific Fleet in 1942 at Pearl Harbour, large numbers of ships were sent through the canal to reinforce them.
But it was their ascension in power during WW2 that meant they could now afford to build a fleet for each theatre, and not move it around. They could now expand their aircraft carrier decks and armour them.