Just a few things I'd like to add.
Far as OP's question. The Colorado and New Mexico would have suffered the same fate as the Repulse and Prince of Whales. In 1941 the anti-aircraft batteries on battleships werent nearly as extensive as they were in later years of the war. Plus the fact they had zero air support. They were even less armored as the Prince of Whales and she still met her demise.
Second. While maybe considering a "bomb", the shell that hit and sank the Arizona was a 16" armor piercing artillery projectile used in the Nagato's main guns that was equipped with aerial stabilization fins. This instance along with the mentioned scenario of Billy Mitchell sinking the Ostfriesland with aerial bombs and the 10ton "Tall Boys" used against the Tirpitz are among a rare occurance to Battleships. Couple things to consider is that in those circumstances the massive bombs used were only able to be equipped on high altitude bombers, not the nimble dive bombers, against stationary targets. While at sea high altitude bombing proved inaffective against moving ships. Dive bombers and their relatively small bombs (250-500lbs bombs) did only superficial dmg to battleships (South Dakota was hit with such a bomb and they just swept the debris over the side and kept on trucking). But rather was highly effective against the lightly armored decks of aircraft carriers. Which is the main reason why the newer fast Battleships massive anti-aircraft armaments was brought to bear screening for carrier tasks forces while the older battleships spent most of their time shellacking island fortifications for Marine assaults.
The biggest threat to all warships was torpedos. Thus the reasoning for the layered screening with several dozens of destroyers, light and heavy cruisers and then battleships forming a circular net around the carrier groups in massive 75+ warship flotilas. In the latter half of the war the sheer number of escorting ships, the increased volume of AA battery, the advancement in radar and fire control technology made AA quite effective against low flying Torpedo and Dive bombers that got through the Combat Air Patrols with our Hellcats and Corsairs just slaughtered pretty much everything in the air. We seen what happened without those resources readily available earlier in the war with the loss of the Yorktown, Lexington, Hornet and Wasp (leaving the Enterprise as the only functional Carrier in the Pacific till the Essex's started rolling out).
While Kamakazi's did account for 32 ship sinkings off Okinawa, none of which were captial warships (even though some had been struck). Even the ones badly damaged like the USS Franklin, USS Bunker Hill..etc all made it back home under their own power. So the Kamakazi was pretty much non-effective towards detering the US forces.
But all in all it took a collective arsenal of aircraft and warships for the Navy to effectively function as a whole. Not really one thing overshadowed another as each had their own purpose and did it well. Same can be said about todays Navy. As mighty as the Nimitz class is, they still need ASW/Anti-Air/Anti-surface protection from the Arleigh's and Ticos (and the fast attack sub thats dispatched with every carrier battlegroup) as they simply can't survive a multi-faceted attack on their own. While projecting massive firepower they are just as vulnerable as carriers were in WW2 without help.
