Both Barham and Royal Oak were designed and laid down before WWI, so I don't consider them "modern" by WWII standards. Carriers are not battleships, so they don't count on sub vs BB.
1. Then there weren't very many "modern" ships. By the time WWI started torpedo protection was already quite advanced, the largest leaps in technology occurring between the turn of the century and around 1910. Those ships were also launched mid-WWI so you need to take that into account too, the design they're laid down with is not always the one they're launched with.
2. The point was about capital ships, not just BBs.
3. The Eagle and Courageous were both converted carriers, which bore the torpedo protections of their predecessors.
About those two BBs, Royal Oak was torpedoed on anchor, so she was an easy target. After WWI she had got torpedo bulkheads retrofitted. Royal Oak was first hit with one torpedo that had practically no effect. After hearing the explosion and not knowing what it was, her crew did not make alarm in Scapa Flow, but went back to beds! The sub turned and fired a miss with aft tube, turned again, reloaded forward tubes and then got three more hits that sunk Royal Oak. If it's crew had done something after the first torpedo hit, like alarmed a destroyer ormoved to another anchoring place, she would not have sunk.
A BB moving at convoy speed is also an easy target. You also seem to be moving goalposts here. The point was never about whether crews did the right things in battle or not, so I fail to see how that's relevant. The point is the following:
1. Surface raiders at-large force the British to escort convoys with enough firepower to fight these raiders
2. These escorts will be capital ships
3. Since these ships will be unable to move at their normal speeds, rather at the much slower convoy speed, this will make them vulnerable to submarines
You countered by saying that modern capital ships would have torpedo protection that would prevent their sinking by submarines. I'm still waiting for you to show why that's the case. There are several examples of relatively modern capital ships being sunk by submarines. The point is not what, precisely, the torpedoes did to sink the ship, the point is not how many torpedoes were fired (I mean seriously, what Uboat captain worth his salt is going to
not fire a full spread at a freaking battleship!?), the point is not whether the destroyer crews properly detected the submarine.
I found information claiming that explosion was caused by her 4 inch ammo being stored on corridors next to main magazines, instead of purpose built 4 inch ammo magazines. If that is true, she might have survived, if ammo was properly stored. Has anyone read HMS Barham's Board of Enquiry report?
That was something very common in the Royal Navy, and was the cause of the British losses at Jutland as well. Basically the idea was that if your ammunition was more accessible, you get more shots off more quickly, winning the battle before you get hit. It's a gamble that allowed the British to have unparalleled speed in firing their guns, but left them vulnerable to flash fires.