It doesn’t save our captured people from torture. But then again, neither does not torturing our captives prevent our people from being tortured. See, e.g., Berg, Nick (we haven’t sawed off our prisoners’ heads, and yet his head was sawed off).
But if we’re just arguing philosophically, I’d point out that the costs of fighting against an enemy that tortures its prisoners would be higher than the costs of fighting against an enemy that gives its prisoners hot chocolate and fluffy pillows. Thus, a country that tortures its prisoners might be less likely to win a popularity contest, but people would be less likely to fight against them because they’d be more likely to suffer great pain and death
I have no cite for this proposition, but then again, you don’t have any cite for the proposition that torture makes people more likely to fight against us.
As for torture leading to charges of hypocrisy, my immediate thought was, “Who cares?” But the reason that we’re not being hypocritical by leaving an exception for a ticking time bomb scenario is that the situation in which we’d allow torture is not morally or ethically equivalent to the situations in which our enemies use torture. We’d use torture when it will save the lives of many people that would otherwise be lost, and no other methods will suffice to reveal the information. The folks that we’d be prosecuting would not have used torture in those situations.