The biggest problem with evaluating people skills is that you need to have interviewers properly trained in doing this. Otherwise you end up losing a lot of diversity due to different thinking and cultural expectations (not to mention people who are good at lying). Being a person that has failed many interviews solely on the "people" skills aspect, let me explain the dangers of heavily evaluating someone on this:
Amazon: "The reason you stated for wanting a new job wasn't: To advance my career. Instead you said your previous job wasn't working out which is a sign of someone who runs away from problems" (Amazon normally doesn't tell you why you weren't hired)
Reason I was basically fired from Amazon (after went from contractor to full time): Not influencing groups outside your own within the company in adopting invocations you created and unable to solve the fundamental communication problem between the developers and testers.
Blizzard: My answer to "If you and another developer have an equally good solution to a problem, which one should be picked" was "flip a coin". The correct answer is "Let's go with your solution this time, and next time we can do mine". Reason for not being hired: Unable to handle conflict (which is right, I can't).
Other companies I interviewed for wouldn't say the reason for not hiring even though I did just fine on the coding parts. I think they just didn't like me. I eventually got another job though a diversity placement program.