That works if you assiduously and diligently and without flaw, start paying attention after no more than the third time you hear the idea advocated, and without using the idea itself to judge untrustworthy those who otherwise see competent.
In practice, people usually reject the idea itself and go on rejecting it, when they claim to be acting under cover of rejecting people. Consider those who die of rejecting cryonics; consider what policy they would have to follow in order to not do that. What good is it to quickly reject bad ideas if you quickly reject good ideas as well? Discrimination is the whole trick here.
I suppose we might have no recourse but to judge people and shut our ears to most of them, in the Internet age, but to say that we "lose so little" far understates the danger of a very dangerous policy.
I agree that people often don't make the necessary distinction between ideas they have evidence against, and unevaluated ideas they've been ignoring because they've only heard them advocated by kooks. As you point out, only ideas in the prior category properly discredit their advocates.
Tyler Cowen argues in a TED talk (~15 min) that stories pervade our mental lives. He thinks they are a major source of cognitive biases and, on the margin, we should be more suspicious of them - especially simple stories. Here's an interesting quote about the meta-level: