With respect to your point about unstructured interviews - keep in mind that any statistical measure of performance isn't based on an objective measure of output - it's almost certainly based on performance ratings, which take into account "impact on the entire team." If anything, my experience is that charming, likable people that do well in unstructured interviews are also better at getting better performance ratings than they deserve.

Also, I think you're implicitly assuming that structured interviews cannot measure soft skills as they relate to workplace behavior. I would argue the opposite - the only way to ensure high standards for these types of skills is to have a structured interview. Otherwise, you're not systematically trying to hire people whose workplace behavior enhances group productivity, you're just hoping that whatever random biases that interviewers bring to the table end up being a net positive. Being a productive team player isn't about being able to impress a random person in an unstructured conversation - it's about knowing how to behave productively (combined with the willingness to do so, which unfortunately is contextual and virtually impossible to directly observe) in a wide variety of challenging situations.