How about sports and fast paced games?
Players are often required to make decisions with no time whatsoever to plan. For example, you might find yourself surrounded by enemies with no warning.
You need to know whether to run on foot, to teleport away, or to fight.
The difference between reacting in a third of a second and a fourth of a second could mean life or death.
Success in this situation, assuming it’s possible, is dependent on your experience in similar situations and your instinctual reaction. Since you do not have the time to think, your decision is almost guaranteed to be imperfect, but any improvement in it is highly beneficial.
Obviously, the same would often apply in war or in certain crisis situations.
You mention lots of fields (computers, math, science, engineering) where your argument is almost tautological: in a case where you have time to reconsider each decision, a slow but reliable and precise method is better than a snap judgment. Yes, I would agree with you, and I would also agree that logical thinking is better than intuitive thinking in many, many situations.
Are you suggesting that the ability to model others or respond to nonverbal cues is innate, rather than learned? I would definitely disagree, though proving it would be difficult. I suspect that it’s a matter of internalizing the results of numerous actions and reactions in different situations. In my experience, it’s often developed by people who travel lots or are otherwise exposed to tons of different people in a situation where being friendly and getting on their good side is very helpful. Some of them, pretty bad at socializing before they were in such a situation (and really gave it the necessary effort to learn).
I disagree, however, when you say that being socially successful is innate.
The advantage of gut feelings and intuition lie with their ability to synthesize years of experience and thousands of variables into one answer within less than a second.
When is this necessary?
During a conversation, someone watching your face is going to be observing how you react (even in the smallest possible ways) as they speak. You don’t have an hour, five minutes, or even two seconds to decide how to present yourself; they’re going to judge you based on that instantaneous reaction (or a lack of one, including a delayed reaction or straight face.)
Anyone who is a natural “people person”—the kinds of people who can get almost anything they want from anyone around them, who make great salesmen or politicians—is going to need to be able to continuously react “properly”, and that means intuitive judgments.
Same thing with any kind of games/sports, or literally any other situation where a quick reaction is required and not immediately responding will doom you no matter what.