Bounty was well suited to weather the storm she faced. Square rigged wooden vessels endured high seas and winds for centuries. While many were lost, it was almost always a result of being driven on a lee shore and breaking up on the beach or on rocks. So long as she has water under her keel and maneuvering room, she should have been fine.
However, she wasn’t a truly historic vessel, she had a diesel engine and probably relied on her engine rather than sails to maneuver. I cannot tell from the picture, but it looks like she did not have any sail set (she would have staysails only and perhaps a foretopsail). I could make out a yardarm and it does not appear to even have sails bent. If she had no sails bent, then when her engine failed she was doomed. Her crew was inadequate to get sail aloft, man the pumps (did she even have chain pumps) and do other things that a square rigger must do to weather a storm.
I suspect that she lost her ability to steer, came athwart a wave, broached to, and shipped water through her hatches.
reliant on modern technology (electronic pumps) which failed
I think you paint a persuasive scenario. However, Bounty’s master, knowing that his crew was incapable of managing the vessel under storm conditions, especially if diesel power were to be lost, made a foolhardy and unseamanlike decision not to seek safe harbor. Running under bare poles in extreme conditions, he gambled his ship and crew on the expectation of not losing power. I am very sorry for this loss, and do not understand, given the abundant advance warnings, why a more prudent course was not taken.