I think the point is that such a mind-killing problem doesn't answer anything. A reasonable person may say "both puzzle options are awful, I don't want to play", but that doesn't mean that the same person can't give a moral argument for action or inaction in a more realistic situation.

"a crucial part of that is getting people to adopt an identity of critical thinking"

What to do about folks who believe/trumpet that they have adopted such an identity, and use this as a shield against conflicting arguments?