I'm sorry to hear about how stressed you get during interviews, but unfortunately the stress you demonstrate during technical interviews is a useful heuristic when determining whether or not a candidate would be a good fit for a company. Is a good signal all of the time? No. Is it a good signal most of the time? Probably.
And that's coming from someone who enjoys interviews, because I'm almost always smarter than the other guy (and it's usually a guy) interviewing me. Every job interview I've had has resulted in an offer.[1]
But their unique and outlandish nature sets them so far out of anything experienced in a job situation, except possibly for sales. Trying to give them the meaning you're going for is rather pitiful given you're so earnest!
[1] For similar reasons, I generally decline to interview prospects, because I'm afraid I judge too narrowly.
Sorry, you're so completely wrong it's painful, unless one of your company's core competencies needs to be semi-confrontational meetings - if you're a consultancy, for example, or you're a wildly dysfunctional company. Social anxiety correlates pretty well with being in a STEM profession.
Probably not a good signal because company interviews tend to slip naturally into the human tradition of group initiation rites, unconsciously testing things like social hierarchy, fitness, dominance, loyalty, in addition to the stuff that really matters like problem solving. Technical jobs today simply don't require the strong social interaction and group selection that hunting for food and fending off wild animals did.
I really can't imagine what would lead you or anyone else to think that's a good signal. I guess maybe it could possibly be good if you're hiring someone to do cold calls or something.
Neither of us have statistics on that, so a yes/no battle here is pointless. I and many others find it to be a useful signal when someone demonstrates intense anxiety under pressure, you and many others do not. Agree to disagree.
If your programmers are having to work under pressure then you're doing it wrong. It is the job of the manager to create an environment where people are as effective as they can be, and creating artificial space for developers is part of that. (Read Peopleware for more on this.)
If you're only willing to consider people who can somewhat function under artificial pressure, then you're passing up a lot of top-notch candidates for very bad reason.