I don't believe we are, because I know of no evidence of the following:

evolutionarily speaking, a big function of system 2 is to function as a decoy/shield mechanism for keeping ideas out of a person. And increasing a person's skill at system 2 reasoning just increases their resistance to ideas.

Perhaps one or both of us misunderstands the model. Here is a better description of the two.

Originally, I was making a case that attempting to reason was the wrong strategy. Given your interpretation, it looks like pjeby didn't understand I was suggesting that, and then suggested essentially the same thing.

My experience, across various believers (Christian, Jehovah's Witness, New Age woo-de-doo) is that system 2 is never engaged on the defensive, and the sort of rationalization we're talking about never uses it. Instead, they construct and explain rationalizations that are narratives. I claim this largely because I observed how "disruptable" they were during explanations--not very.

How to approach changing belief: avoid resistance by avoiding the issue and finding something at the periphery of belief. Assist in developing rational thinking where the person has no resistance, and empower them. Strategically, them admitting their mistake is not the goal. It's not even in the same ballpark. The goal is rational empowerment.

Part of the problem, which I know has been mentioned here before, is unfamiliarity with fallacies and what they imply. When we recognize fallacies, most of the time it's intuitive. We recognize a pattern likely to be a fallacy, and respond. We've built up that skill in our toolbox, but it's still intuitive, like a chess master who can walk by a board and say "white mates in three."