If you can't code under pressure, you aren't a very competent programmer. Real world projects come with high pressure scenarios for software engineers. Code monkeys may be able to get away with low pressure, minimally impactful projects.
The thing is, it's a vastly different kind of pressure. When I am coding as part of a job - by myself or with others - there is no inner monologue in the corner of my brain doing something like this:
"Could do that or... no damn, that's O(n^2), damn I'm taking too long that one looks bored, if I instead put those keys in a hash... no, I'm sure there's a better way, running out of time though, is he looking at his phone now? Okay, what was the profile of merge sort again? ... oh, shit! She felt like she had to offer me a guiding hint, I'm doing it wrong!"
And it never stops going. It picks apart every choice I make, and by five minutes into the interview I come across as a sub-articulate mess.
In no other high-pressure situation does this happen to me. Hell, this past summer I actually spoke at a conference and I didn't have the kind of trouble I do in an interview.
Whiteboarding, paired coding, participating in architecture design - these things come easily. In the context of an interview, though, it goes out the window.
That kind of scenario happens to me daily.
If you learn something from someone, is it that much trouble to give them credit for expanding your horizon?
If this mindset is recursive down your organization's hierarchy, doesn't it create a scenario where a legitimate critique never gets heard because people don't question the decision of a higher ranked employee because there is the impression that they know more than you?
Seems like you and your employer are worse off, but your ego remains intact.
Code now or die isn't usually something most people face in their day job.
If that happens consistently for months at a time, then as said the PM is severely fucking up. And if that wasn't communicated as an expectation before compensation was negotiated, then the company is probably fucking up.
As the quip goes "If a race doesn't have an end, then it's a death march."
B) If you're working a job like this you're working a shitty job and ought to quit. Unless you're maybe hacking the Gibson to stop some oil tankers from going belly up there is hardly a reason in our industry for this kind of shit.
But I will not work in a company where that's the norm.
I value my health more than the potential money from that stressful job.
Not all jobs give you all the time in the world on a test server without interruptions.
Performing well in this kind of scenario is much less about algorithms and data structures, and much more about systems thinking and the level of your understanding of your system.
System knowledge and knowing which one bolt to replace or turn is almost always more effective.
PS: Not to mention, if we're getting into algorithmic complexity levels of engineering on a monkey patch to a production system, then so many alarm bells are already ringing.
An interview situation is much more adversarial: They are looking out for reasons not to hire you, you are competing with others for the job and only one can get it! No such consideration on the job, unless the work environment is completely and ridiculously broken. When are you ever in a work situation where several people work on competing solutions and everybody else but the person who made the winning one is fired? At work you are working together, and to solve a problem, not to week you out of the pool.
If there's ever going to be a situation where something costs $100k/hour if it's offline then you have 5 test servers and 2 or 3 load-balanced production servers so a failure doesn't take you offline, and you've written procedures and processes to handle critical problems long before they happen.
You definitely don't try to hotfix things while the foreman complains. That will make things worse.
Also...these situations can be trained for to certain degrees. There's well established precedents in crisis management. If you write code for a customer with a 100k/h downtime risk you should have done a very thorough risk analysis and have mitigation plans for most scenarios. The unknown unknowns that can happen are obviously the hard cases but you should be able to justify that these are going to be expensive no matter what. But even for these cases bricolage is trainable to a certain degree.
If you know there's 100k/h costs of failure you should also very specifically mention the fact that you are looking for these stress coping skills in the job description (and as such the interviewee should be prepared).