I may be mistaken, but, IIRC, the type 285 radars were not functioning properly at the time of the battle... Thus, the 5.25" guns were of limited value...
We know the 282s, which ranged for the pom poms were not functional. I'm also pretty confident that the Type 273 surface search was not fully functional. The Type 281 was functional as tracked the approach of the Japanese aircraft.
The 5.25s did damage several of the torpedo bombers of the second wave. So apparently they were close but not close enough. During the first wave the 5.25s were thrown off by POW's manouvering. After the second wave the list and the power outages combined to essentially take the 5.25s out the fight.
Also, PoW was not alone, but in company of Repulse and 4 DDs... But it's true that neither of the 5 escorting ships possessed serious AA capabilities...
It was only three DDs. Tenedos had been detached to re-fuel the previous evening. One of the DDs, HMAS Vampire, had no real AA capabilities. The others were Express and Electra with 12cm guns. The Repulse's AA was as you say, not much. Its six 4" guns were completely manually operated so they could only lead very slow aircraft, and they could not be depressed enough to engage torpedo bombers. It had been equipped with three sets of pom poms. During the fight Repulse's Pom Pom's all jammed from faulty ammo.
in better company (say 1 AA cruiser and 1-2 modern CLs, and 6-7 well armed DDs), and with all systems and weapons operational, PoW may have been better off that day... But I doubt it wouldn't have been sunk.
I'm a little comfused, because what you outline here resulting in POW still getting sunk is close to what the American BBs had in the Solomons with weaker flak or probably equal flak to POW. How would you say NC or SD would do substituted for POW on Dec, 10, 41?