History will strongly disagree as those older battleships were heavily modernized with the same radar, fire control and dual purpose secondary guns of their younger fast battleship compatriots.
By the end of the war, yes. Less so at the start.
Sticking just to the US Navy, the older single purpose 5 inch guns were removed and replaced with the newer 5 inch dual purpose guns during the Interwar period and before Pearl Harbor.
They also put dedicated flak guns on the South Dakotas but the (iirc) 8-single mounts with some fifties and Oberliks were woefully inadequate for pacific action. They could barely screen themselves let alone make more than a token contribution to air defense.
US Navy determined that anything less than a Bofors was practically worthless for air defense, but by the time they learned this Jets were around.
Sub-hunting is the business of destroyers, destroyer escorts, carriers, and light cruisers, not battleships. As sonar generally isn't installed on most of them.
Sonar for battleships was mostly as defensive measure, and I guess I should have said (strictly speaking) Hydrophones. I don't even think they had depth charges, but knowing a sub is out there, or getting a warning of incoming torpedos, could be the difference between survival or sinking.
Those "gun barges" were extremely valuable to the guys on the ground calling in gunfire support. Whether for precision strikes on the target(s) and to provide suppressing fire halting the movement of the enemy.
Correct, but they weren't directly helpful in fleet action. And for the IJN, that both directly contradicts the original point of this tangent AND they lacked the speed and endurance to chase targets.
Remember this discussion originated out of whether or not the IJN fucked themselves by building battle ships (as an offshoot of ISDs and WWII in space). I was pointing out that the IJN was right to build battleships, that even though they didn't really get to engage in a truly decisive surface battle, just by being heavily armored and heavily armed they shaped fleet actions by the nature of existing. But the IJN build the wrong sort of battleships and used them wrong.
The US used battleships (and cruisers) to devastating effect on land-based targets, especially since many south pacific islands had no place out of range of the big guns. So even if they were largely just serving as deterrents for anyone trying to gun-run the carriers, they could do something useful.
The IJN, who this was originally about, were not allowed to use their battleships for shore bombardment - half out of ego, half out of the difficulty of replacing the barrels of said guns. So in their case, their battleships were just ships-in-being.
edit:IJN battleships also lacked the speed or endurance to outrun anything other than another inter-war battleship. interwar, even early war, this would have been less of an issue in the south pacific where islands and lack of quality RADAR (and commanders who distrusted it) would have made ambushes possible (and Japan wasn't on the extreme wrong end of the ship numbers to make flushing quarry a viable tactic) but by mid-war between Radar and recon aviation (and for the US, broken encryption) that wasn't a possibility anymore.
Most of the US battleship fleet also lacked this ability. But the Iowas had enough speed and endurance to chase a carrier and enough air defense to very likely survive their airwings. But there was never any need for that by the time they were launched though.
