Obi,
I would argue that although no longer an antiship threat the 6inch guns of the Belgrano would have been a serious threat to the Infantry forces on the Falklands, much like how the Royal Navy shelled the Argentine garrison.
What are your thoughts on that?
Certainly those guns posed a serious threat to troops ashore, and they had greater range than the British 4.5" guns used for the same task. The troop landings were still some weeks away at this point and the immediate threat was to the carrier Battle Group, against which the Argentina Navy had deployed their fleet in a pincer movement, with the Belgrano and two Exocet-armed destroyers to the South of the Falklands and the Carrier 25 de Mayo with two Type 42 DDGs forming the Northern pincer. The Submarine HMS Conqueror had been trailing the southern group for some time, whilst HMS Spartan was in contact with the Carrier group. She lost contact though, leaving only the southern group as a definite target. Low winds prevented the fully laden Skyhawks from being catapulted off the carrier so the attack was postponed for 24 hours, with the Belgrano group sailing in a holding pattern (leading to later false accusations that they were returning to port). Belgrano's group were about to sail into shallower waters (Burwood Bank) where Conqueror couldn't follow, so having lost contact with one half of the impending attack there was a chance we could lose contact with the other half.
RN Submarines were under direct control from London, not operationally a part of the Task Force. Adm Woodward was well aware of the threat both groups posed and being a former submariner himself understood the situation only too well. He sent an order directly to the Conqueror to sink the Belgrano, knowing the order would be intercepted by Northwood and cancelled, but he did it to impress upon his superiors just how important it was. It worked, and shortly afterwards the order to sink the Belgrano was issued by Northwood and the rest is history.
After the sinking, the rest of the Argentine fleet returned to base and didn't put to sea for the remainder of the war, so both tactically and strategically it was very successful for the British side, taking the Argentine navy out of the War at a single stroke.
The ARA General Belgrano DID pose a significant threat to the ships of the Task Force. Fifteen 6" guns in five turrets. All of which could outrange every gun in the Task Force, and none of our ships were fitted with armour. The words 'Knife through butter' spring to mind, as I'm sure they must have been on Adm Woodward's mind too. If she had attacked in bad weather (common in the area at the time) there is a good chance we might mot have been able to get Sea Harriers in the air, and at the time they could only attack her with free fall HE 'Iron' Bombs, not armour piercing, so to repel a WW2 Cruiser we would have to have employed WW2 tactics, dive bombing at close range in the face of a barrage of 40mm Bofors fire and sea Cat SAMs. We could have launched our own Exocets at her from some of the Frigates and Destroyers in the TF, but she probably had chaff launchers too and if she had penetrated to gun range she can inflict a lot of damage before she's taken out. Add in her own escorts lobbing Exocets at the TF, with Skyhawks attacking from their carrier and the outcome is far from certain.