>No, they don't. For that to work, this requires the proponents of bad ideas to respond to logic

You're missing what's at stake here. It is emphatically not to convince the speaker he is wrong. Often times they have ulterior motives at play that prevent them from recognizing or acknowledging that they were wrong. The point is to convince those who are on the fence or otherwise could be persuaded by the bad ideas. Seeing someone like Milo get pummeled in a debate does incredible damage to his brand and his ideas. It may do absolutely nothing to convince Milo he's wrong, but the ideas he's espousing now have resistance in the minds of potential followers.

Give potential followers the mental tools to resist the appeal of these messages, and the ideas die out with the hardliners.