Worldliness seems impressive to the unworldly, but it's very easily acquired. So don't overrate it. It's worth something, but not much. It's infinitely more common than knowledge and insight.
YC, for example, cares way more about how much knowledge and insight you have than how worldly you are. They know that starting a startup is a crash course in worldliness. You may be a reclusive nerd at first, but you'll be plenty worldly after a year or two.
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