People calling for Cook to be stripped of captaincy are ignoring the main point, which is that he has been massively let down by his team. It doesn't matter how good a captain is, if the fundamentals- good, in-form, fresh, and motivated cricketers- aren't there, then the team is going to be brutally punished, irrespective of how many slips you pack in.
Michael Clarke is often considered the best captain in the world. Was his captaincy winning Australia matches in India and England? No. Could Steve Waugh, Mark Taylor, or Allan Border have won any of those matches if they captained instead of Clarke? No. If you haven't got the players to begin with, no captain can ever make a difference.
Finally, Cook isn't the problem. Flower is the cancer, all Cook does is follow orders. Flower brings a Zimbabwean, minnow mentality of avoiding defeat at all costs. A school of thought where a draw is as good as a win. He, along with the rest of England's backroom staff, pride themselves on some sort of cricketing equivalent of marginal gains, where everything is 'scientific' and run through the computer. That's all England have done, run cricket through a stats computer, under Flower. Chris Rogers scored 45 runs today through third man. Not once did England place a man at third man when he was batting, because when you run cricket through a computer, third man, statistically, is not one of Chris Rogers' favoured scoring areas. It didn't matter in the slightest to the Zimbabwean Sir Brailsford that Rogers had creamed 9 boundaries through third man, the computer said that Rogers, I dunno, gets all his runs from ugly T20 slogs to midwicket or something.
Approaching the sport like they're playing International Cricket Captain 2013 is also why when Jade Dernbach serves up his full toss leg stump filth in ODIs, England have fine leg up inside the circle.