Honestly, the way you conflate soft skills with randomness and capital-P Politics is worrisome.
> Every single thing that you listed requires a understanding of the opposing party that you just talked about in order to make the deal work out.
Yes, that's the whole point! Understanding other people is an important life skill, and something that every neurotypical person should be able to do. (And, if you're not neurotypical, it's a limitation about yourself that you need to acknowledge)
See it this way: You have two people in your team who disagree on a technical issue. You need to help them come to a decision. Would you rather have those two people have the mindset that "other engineers have their own preferences and that sucks", or that they have the mindset that "other engineers have their own preferences as a result of their own experience, and I welcome navigating those differences as part of the job"? Which of those two conversations ends with the two engineers understanding why the other person has a different opinion, and reaching a reasonable compromise? Which conversation ends with everybody involved learning something new, making the team technically stronger?
