Reply: baseline social comfort is not a generic personality type.
Seems like you just want one generic personality type on your team to make your life easier.
You should really give anxiety sufferers a shot. There are some real gems there which you are dismissing out of hand.
It's not that their anxiety is crippling; it's that for various reasons, the hiring process is typically conducted in a way that is at best often careless and inconsiderate to the candidate -- and quite often needlessly stressful and confrontational.
In other words, the people who sometimes get tripped by such processes aren't demonstrating "crippling anxiety"; they're demonstrating perfectly normal, human traits.
Plus you literally just came out and admitted that it's not actually about measuring technical skill, it's some run-you-through-the-gauntlet "attitude" bullshit. Gimme a break.
Whiteboard sessions are typically done standing (an unusual posture for most people), in a non-interactive environment and importantly, in front of other people (which is quite different from coding, alone, in a development environment, in the sitting or standing posture of one's choice). Who also expect you to explain to them what you're thinking as you're coding, interrupt you with questions or hints, etc. An entirely different workflow from just sitting down and writing code.
Even so -- traditional whiteboard sessions might sort of be OK, if they kept it to a single hour. The thing is, these days, the sessions (whether using a whiteboard per se, or some tool like hackerrank) can typically go on for multiple hours, like 4-6, being stared at by 5-10 people throughout. And are sometimes very poorly coordinated (either the problem isn't properly stated... or it seems no one bothered to check that you've already done the first 2-3 hours of "idiot testing", and make you do it all over again when you get referred to another team, etc).
And this sometimes on other pointless exercises (like a full hour of solving pure logic puzzles, being administered to you by a fresh graduate).
At some point it just gets to be unnecessarily exhausting and humiliating. And no, it's not a symptom of an "attitude problem" if one starts to feel less than enthusiastic about the way some companies conduct these sessions.
That entire process many only produce one or two sheets of paper, with many more sheets ending up in the bin, but I find it is time well spent as it makes the coding step much easier.