You're either missing or conveniently ignoring the fact that almost all deadlines are artificial, and the only thing that happens when they get missed is that someone's quarterly plan doesn't match up to reality. I had a whole bit about that written up in my editor that I decided not to include, but, needless to say, reality disagrees with you here. Software projects are notoriously late, and people generally don't get fired as a result. Your other scenarios of "site down" or "customer system compromised" aren't even examples of time pressure, so I have no idea what you were even getting at.
Oh, and if you look like a dogmatic jerk in front of an audience, there's nobody in the back row waiting to make a mark on your permanent record as a result, just so you know.
But, back, now to interviews. I've been in I don't know how many interviews (hundreds, easily, if we
count both the ones where I was the interviewer and those where I was
the candidate), and I can tell you for a fact that time pressure,
performance anxiety, and every single other thing I've mentioned
impacts people's interview performance, and does so in such a way that
it wouldn't be relevant on the job. I could even cite research to
that effect if you like.
For
whatever reason, you're now so out of touch that it's absurd. I had a whole point by point refutation of every single thing you wrote here, because for the average individual, it's totally wrong, and it would cause them harm if they tried to incorporate what you wrote into their world view.
Maybe you truly don't feel the same type of anxiety in technical
interviewers that most people do. Fine. The fact that you're (a
robot, a Zen master, financially secure enough that having a job
doesn't matter, a 99th percentile 10x programmer who crushes technical
interviews with both hands behind your back and using the whiteboard marker in your teeth, or whatever it is that makes you feel this way makes you
not qualified to give advice on the matter to typical, average people.
TL;DR: No. Just no. I can tell you're not going to convince me of anything, and I suspect I can't convince you of anything, either, but my conscience just won't let me let this go unanswered.