A job interview, for me, still brings out the nerves, even though I don't get nervous on stage. I think this is because improvisation has never been my strong suit. Even though you could make a case for a job interview being like a performance, there are some very important differences. For one, the interviewer is the only one who gets the script. Nobody is allowed to rehearse, at least not with full knowledge, there is only one performance, no audience, no director and no second chance. To top it all off, the interviewer is half trying to help and prompt you, to a degree, but also half trying to trip you up and make you fail. It's adversarial improvisation with unequal preparation and real consequences, but only on my side of the table.
The whole interview process is set up to favour people who are strong personal communicators face to face and that's it. Unless that's the job, I think you should find a better way to test actual job skills rather than interrogating someone whose job is going to involve staring at a computer screen most of the day.
Mokalus of Borg
PS - I've had some companies screen by programming puzzle.
PPS - They were the best ones.