I agree with your point, that a certain level of social skills is a must, although in my experience, when people start competing over making the best impression

I agree with your point, that a certain level of social skills is a must, although in my experience, when people start competing over making the best impression, many choices that improve it would be disadvantageous when it comes to execution. The simplest example I could think of is typically being relaxed and simply agreeing with everything that your opponent says gives better surface impression than being focused on understanding your opponent and actually trying to defend your point (the classical salesperson vs engineer case). Except that approach would deadlock your execution, but nonetheless I see many people successfully using it to gain one's trust and get preferred over someone who pushed back too much.