Well, first off, there are 'splinters' and then there are 'splinters!' By 'splinterproof' we are really talking about falling shell fragments from AA, stray bits of shrapnel metal flying around, and machine gun bullets. Looking at the main turrets of say, 'Atago,' there is only 1" armor for the turrets! That won't stop a 20mm round, let alone a chunk of steel several inches thick and weighing 50 Lbs or more from an exploding 16" shell, or even a chunk of the ships own armor flying into it either. And a Japanese 6" turret will have no more armor than that.
You mention that the fire control center is below the armored deck, yet 500 Lbs and 1000 Lbs dropped on Yamato (just dropped, not a ballistic shell plunging in with enormous velocity) went right through the armored decks and trashed the ship from stem to stern, one of which, landing between a forward 18" turret and a 6" turret exploded with enough force to completely dismount the 6" turret, even though it was not a 'direct hit.' Concussion alone is enough to shatter the optics of a fire director, even if it is not hit directly. In fact, Yamato, and a few other battleships like HMS Rodney had a lot of problems with the concussive effects of their own main guns firing, so bad that the bridge and other structures could be severely damaged if the guns were aimed much further aft than directly broadside, and tear up the foredeck if aimed too far forward as well. Yamato in particular was very bad that way, and no-one could be on deck if the main guns were firing, regardless of direction. That means, if there is a fire someplace, the fire control people are not going to be able to get at it from the deck, if the guns are still firing. I have not heard of any such problems with the Iowas, though thier blast is pretty prodigious as well.
On another point, all of these directors, and the gun turrets as well, depend on electric, or hydraulic power to operate, and electrics for communication. If a 16" shell penetrates the superstructure and explodes inside, it is going to cut power lines, live steam pipes, hydraulic lines, and start fires (even the paint will burn merrily in such circumstances), and these things will have a cumulative and cascading effect that is geometric, not arithmetic, and I don't care how well 'armored' the conduit pipes are, they WILL get cut or burnt, and in such situations, it is surprising how often such damage either cannot be bypassed, or got at for quick repairs. Fire, as you may recall, burns upward for the most part, so a nasty fire below the bridge, for instance, can produce enough smoke to obscure observation for the whole tower, or even make the bridge, or anywhere on the tower be completely untenable in very short order from the heat of the flames. This used to be quite a problem with a number of ships in WW1, whose masts and bridge structures could be severely affected just from the smoke of their own boiler furnaces, let alone fires caused by battle damage. As well, not all fire-directors are equal, with the most accurate being those with the widest binocular 'field.' Thus a fire director whose optics are 40' apart, will be far more accurate at long range than another director whose width might only be 12'. Hit the big one at the top of the tower bridge, or make it inoperative, and the other big one aft, and long-range accuracy will drop accordingly.
Finally, while you seem to think that shells hitting a ship are 'random' in their location, in point of fact, it is amazing how many times ships have had their bridges/battlebridge/conning towers hit directly, and how often hits are made on superstructures and turrets, as against say, the ensign staff or the anchor locker. This is not coincidence. The gunners will do their very best to aim for the center of mass, and a good one will hit just about anything he aims at. Radar-directed firing is particularly suited for this 'center of mass' kind of targeting, and that's where the rounds hit. And that's not just Americans firing, but Japanese, Germans, and Brits too. 'Hiei' was hit dozens of times, by relatively small-calibre shells, and while none of her armor was effectively compromised, or even penetrated, was set on fire, all communications severed, fire direction for main and secondary guns put out of action, and the ship in a sinking condition because electric power failed to run either the fire hoses, or the bilge pumps. Much the same thing happened to Kirishima, and to Bismarck, and the same thing happened to any number of ships, which ended up unable to fight, or run. And if you don't believe me, just ask Admiral Makaroff, Admiral Rodhjestvensky, Admiral Graf Von Spee, Admiral Callaghan, or Admiral Scott..... Oh wait, you can't, because they were all blown away, along with their bridge personnel from direct hits on the bridges of their ships (maybe they should have conned their ships from the anchor locker!)!
As for avgas, any time you have a hangar and airplanes, there will be fuel lying around, along with oil, greasy rags, and all the other impedimentia of airplanes and their mechanics, not to mention all the launches, and other ships boats (made of wood) and their fuels. Yes, the main fuel tank may be down in the bilges somewhere, but there is a pressurized hose to deliver it to the hangar, and a shell hitting the hangar is going to bust up just about everything in there, and set fire to the rest, including any fuel delivery systems. Like I said with the superstructure in general, there is so much packed into a relatively small space, that a hit anywhere on the superstructure is going to hit something significant directly, and will likely affect other systems in the surrounding area as well.
The point of all this is the age-old adage from the Civil War, to win a battle, you have to 'get there fustest, with the mostest,' and most indications are that radar-directed long range plunging fire from an Iowa will hit Yamato before Yamato can hit the Iowa. And if the Yamato gets hit first, chances are, it won't get a chance to hit back effectively, and its chances of doing so go down dramatically with every 16" shell hit she absorbs, even if the armor isn't compromised, even if the ammunition doesn't explode. And since Yamato can't run away because she is too slow, it is the Iowa that has the initiative, and can press the battle, or withdraw at any time (it's like having the weather gauge in a battle of sailing ships)