Part of me wonders if these ideas are pushed by people because it's more convenient for them to push them. Like, if you're a 'brilliant' jerk, it's probably easier to stay employed if people think technical skills and people skills are something of a trade off. And if you're not some sort of genius, it can be comforting to think "well, at least I'm not a jerk/crazy/an awful person".

Same with the dating situation. Must be more comforting to think "I'm not the most attractive person ever, but at least I'm sane and many of the more attractive people aren't" rather than "There are probably people out there who are both more attractive and with a nicer personality".

I also suspect people tend to think everything in life must have tradeoffs, D&D character points style. Like, you have X points to go around in total and if a percentage of that goes to intelligence/skill, there must be very little left over to put into charisma.

You can see that a lot in films and TV shows, where being popular or attractive is often treated as if it's incompatible with being intelligent or a nice person. But that's not reality, and some intelligent/attractive people are also perfectly nice, sane people.