1. Short Answer: Yes, they are very obselete, congress is idiotic for forcing the navy to keep them mothballed.
Obsolete as a surface combatant in a mix it up with other surface combatants due to size an speed.
Not obsolete as far as being a NGFS platform for shore bombardment, with ethier it's main battery or it's secondary battery. It's greatest failing is the cost to crew and maintain an Iowa Class BB, they are not cost effective to the Navy, the USMC would like them back solely for the NGFS role they provide, won't happen.
Only Iowa is in moth balls now, Missouri, New Jersey and Wisconsin are all memorial ships or National Landmarks and are maintained as such. Iowa has a group working to finance her conversion to a memorial ship on the west coast, so the idiocy is over stated in your post.
None will be recommissioned and if Iowa doesn't find a home she'll probably go to the ship breakers in a couple years.
2. Battleships have a comparatively short range, and 16 inch guns have virtually no accuracy compared to cruise missiles or planes.
The range of a 16"50 is 23 miles giving it far and away more range than the standard NGFS direct support guns the 5"38, 5"54 and 5"64 at 14.9 mile max range, without RAP.
For a Naval Gun with the fire direction control system that the Iowa Class had the 16"50 was an accurate system for what it was being asked to do as an NGFS and shore bombardment system, in reality when you are lobbing 9 HC or AP 16"50 rounds at an area target, do you really need pin point accuracy?
From here:http://www.navweaps.com/Weapons/WNUS_16-50_mk7.htm
[FONT=Arial,Helvetica]As modernized in the 1980s, each turret carried a DR-810 radar that measured the muzzle velocity of each gun, which made it easier to predict the velocity of succeeding shots. Together with the Mark 160 FCS and better propellant consistency, these improvements made these weapons into the most accurate battleship-caliber guns ever made. For example, during test shoots off Crete in 1987, fifteen shells were fired from 34,000 yards (31,900 m), five from the right gun of each turret. The pattern size was 220 yards (200 m), 0.64% of the total range. 14 out of the 15 landed within 250 yards (230 m) of the center of the pattern and 8 were within 150 yards (140 m). Shell-to-shell dispersion was 123 yards (112 m), 0.36% of total range.[/FONT][FONT=Arial,Helvetica]The Armor Piercing (AP) shell fired by these guns is capable of penetrating nearly 30 feet (9 m) of concrete, depending upon the range and obliquity of impact. The High Capacity (HC) shell can create a crater 50 feet wide and 20 feet deep (15 x 6 m). During her deployment off Vietnam, USS New Jersey (BB-62) occasionally fired a single HC round into the jungle and so created a helicopter landing zone 200 yards (180 m) in diameter and defoliated trees for 300 yards (270 m) beyond that.[/FONT]
Cost of a Harpoon or Tomahawk is roughly US$ 1,200,000 , are you really going to fire them at every shore target, or are you going to go with the cheaper alternative of an NGFS platform that can range it, given the 16'50 is no longer an option however in most cases within the fan 5" inch NGFS is more cost effective and responsive than air or missiles for target engagement. Sometimes low tech is better, air is not always on station, nor is air always armed to deal with target.
3. The cooling and electricity requirements for railguns currently make them impractical, not sure when that might change, but at current point, they are not.
4. Even if 16 inch guns weren't innacurate, class range, and generally inefficient compared to missiles or planes, the ship that they require is far too large not to be hideously vulnerable to missiles, bombs, and other threats. Doesn't matter if you've got 20 inches of belt armor, a missile can cut through that easy, and sure, point defense CIWS and counter missiles work fine, but you don't need nearly as much of them on a smaller ship
You seem stuck on some preconceived notion that the MK7 16"50 Naval gun is inherently inaccurate for some reason. How accurate do expect a "dumb" system to be exactly? A "dumb" system is only as accurate has it's fire control system and spotters, and human error has to be factored in.
The only real point you have had is that the vessel necessary to support a 16"50 is to large and not cost effective to crew or maintain solely for the sake of having a large caliber NGFS asset, but then thats been the US Navy's point since 1989-90, so I guess thats not really your point at all.
5. An aircraft carrier size is justified due to the massively more firepower than can put out for their size compared to a battleship, in case you ask.
Yeah, good comparison. And I wouldn't ask anyway, but hey . Comparing the fleet air arm, that has been the backbone of the fleet since WWII and a BB that has been pretty much regulated to being a NGFS/Shore Bombardment platform since mid to late WWII is getting into apples and oranges territory. No one is questioning the need for carriers or why carriers are large.
6. I think there is some utility to the 5 inch guns on current destroyers and cruisers as they are relatively small and efficient for the amount of size they take up, and ad a fair bit of versatility for relatively short range fire when I missile might be overkill. They are also smaller and therefore less crippling to the fleet if lost.
Some utility? You think there might be "some utility" to having 5" gun mounts on Destroyers and Cruisers?
Lets put it this way. I know a USN SWO who serves on Ticonderoga Class vessel. To qoute him. "Somes cheaper is better and sometimes guns are more effective." I'll take his word for it.
The USN also still has the mission of providing NGFS to landing forces and a present 5" is what is available. I'd submit to you that you have never witnessed a well coordinated well adjusted FFE on a target from a USN vessel firing a 5" gun against a shore target. And really your gonna launch a missle or sortie a flight of FA18's against every mortar emplacement , machine gun and small troop concentration in the intial stages of a landing? Yeah buddy, thats high tech and all, but hardly cost effective.