Several decks? Exocets come in from the side, aiming just about the waterline - the spot where, incidentally, the armor on a battleship is thickest. An Iowa, or indeed any WWII-era battleship (Bismarck, KGV, Yamato, Vanguard) is designed to take a helluva lot of hits from a bigger shell than the warhead on an Exocet. The only ways to kill a BB from anti-ship missiles are to hit it many times with smaller missiles or hit it with something that can get through the armor, like a Shipwreck. The latter isn't an option to most nations, so you need to hit the big bastard repeatedly.
Furthermore, you are correct in pointing out the fact that most ships in battle die from fire. A pair of Iraqi Exocets did considerable damage to USS Stark, but the crew managed to make that ship both survive and continue to port under its own power. HMS Sheffield died from fire, and it was discovered that the hit immediately severed the high-pressure fire main - a lucky break to say the least. Neither case is going to effect an Iowa, because a ship designed to take a whole bunch of hits is going to not be easily disabled by such a weapon, and there isn't going to be much that can burn outside of the armor belts - the ship's main and secondary armaments are gonna be designed to be protected, and all of the important stuff is gonna be inside the belt.
The main armor belt you are referring to is generally below the waterline. Yes, an Exocet may bounce of off a 16" class A armor belt, but this is not what it is hitting, both because the belt is not at the hull and it is a Class B unhardened belt. It is hitting either a non-armor plate of steel or secondary armor. Momentum alone will penetrate a simple hull wall. The explosive warhead will penetrate secondary armor. Now it will be quickly stopped by the various decks and equipment, and even if that fails the main armor belt. Part of the reason the USA put the main armor belt so low was to give the decks, secondary armor belts, and equipment a chance to destroy the armored tip of the armored piercing warhead.
You are overestimating what is protected by the main armor belt. Yes the main batteries, ammo magazines, and engines are below the belt. Most of the ship is above the belt, and this space is needed for missions. You would have things such as the radar, the electronics, the range finders for the guns, and post WW2 weapons added such as Anti-ship missiles.
The bounce off part is a complete myth. The missile would penetrate the armor into the ship almost 100% of the time. One exocet will not do much damage to a Iowa/Montana, but if hit by 20 exocets, the ships is losing some of its fighting effectiveness, has a good chance of being a mission kill until returned to port (unless this mission is only firing 16" guns under local control), and as hits pile up the possibly of ship loss creeps upward. If the fires get too intense, it will have to be scrapped. After a severe fire, it can literally be quicker and cheaper to build a new ship than to fix the ship. Once the structural strength of the steel is impaired, it can't really be fixed in a practical manner.
Now don't get me wrong. If I had to be on a ship that was hit by 1-4 exocet missiles, I would take the Iowa or Montana over any ship in the USA Navy today, and I would expect to live if not killed in the initial explosion.