"The key to effective intuitive decision making, though, is to learn to better calibrate one’s confidence in the intuitive response (i.e., to develop more refined meta-thinking skills) and to be willing to expand search strategies in lower confidence situations or based on novel information."
and
"Relatedly, it also means we should stop assuming that more conscious and effortful decision-making is necessarily better than more heuristically-driven intuitive decision-making."
I would say that while the article makes very interesting objections to the S1/S2 thinking framework, its objections are that they are far more intertwined as measured. However, the article still very clearly agrees that S1 is lower cost than S2.
The article absolutely does not agree that S1 is lower cost than S2, as the article does not agree that S2 exists at all.
In this representation, "system 1" is simply an early pipeline decision, where one intuitively feels that it is the correct decision immediately. And if a satisfying decision doesn't come up, we keep looping over the decision, adding more factors, until we finally find the factors that make our intuition agree with it and close the matter. The longer we try to find a satisfactory decision, the more factors we try out, and therefore, someone came up with "system 2", but I see "system 2" as a particularly bad misrepresentation: it is still the same system looping, we are just staying in it longer.
The source of my theory is the interesting effect of a broken intuition: OCD sufferers are unable to break from this cycle, and even when intellectually satisfied with a conclusion, they perceive their brains as "stuck" in the question.
So fundamentally, I agree with your general idea: intuition plays a major role in this system, and when it breaks, people get paralyzed in it, no matter how good the decision is intellectually. My only point is that there is no division of systems. It's one single subsystem, integrated with many others, forming one single blackbox entity. The fast/slow thinking framework is a misrepresentation that doesn't really help one understand people's behaviors. It's a bad map.
The point I'm making is, as an organism we avoid utilizing higher-effort or higher-cost actions when unnecessary. An untrained lower-cost (IR1 in the article or System 1 in my definition) decision will result in not caring about quality. A trained lower-cost decision will utilize heuristics to bias for higher quality.