Hiring and interviewing are incredibly broken, I totally agree... And the algorithm puzzles are basically silly and don't tell you any relevant things, like how pleasant would this person be to work with, how conscientious are they, etc.
But.
Usually interviewers are asking these questions to see how you think, not because they expect you to get it exactly right. And so verbalizing your thought process is how you prove yourself. And if you have trouble verbalizing your thought process, I sympathize, but being able to explain to others what you're trying to do and why you want to do it that way is a really big part of the job. And there are going to be a lot of times on the job where you DO need to tackle something wildly outside your skill set, and people need to see that you can at least start iterating towards the right thing. You don't have to be right, you just have to convince them you'd get there in a reasonable amount of time.
Also, if a small amount of pressure causes you to forget your entire CS education, that's kind of relevant to being able to do your job? I'm not trying to pile on to people that have anxiety issues, but being able to do things under pressure is a skill. If we're up against a deadline and you entirely freeze up and can't do anything, that would be a bit of a problem wouldn't it?
It's incredibly hard, and would take years for anyone to come up with any algorithm from first principle. Which means that any test of algorithm is a test of knowledge, rather than "how you think" or "being able to reason about subtle behavior in system" etc. You looks good if you already have the knowledge, and you will look like a clown otherwise. That is okay if you also realize that the breadth of CS fundamentals are incredibly broad and everyone only knows a subset of it (ask as many simple things as you can).
My deadlines are measured in months, weeks and in the minimum, days. There is practically no cases where it is in hours, and absolutely no case where it would be 30 minutes. I (We?) have trained myself to work and deal with deadlines/pressures of those standard time frame, which means that if I have only a day to deadline left, my technical mind shut down and it is now thinking about the business to see what should be best done next.
I believe people would feel more pressure at the risk of failing an interview than the risk of their company's product having a downtime
But.
Usually interviewers are asking these questions to see how you think, not because they expect you to get it exactly right. And so verbalizing your thought process is how you prove yourself. And if you have trouble verbalizing your thought process, I sympathize, but being able to explain to others what you're trying to do and why you want to do it that way is a really big part of the job. And there are going to be a lot of times on the job where you DO need to tackle something wildly outside your skill set, and people need to see that you can at least start iterating towards the right thing. You don't have to be right, you just have to convince them you'd get there in a reasonable amount of time.
Also, if a small amount of pressure causes you to forget your entire CS education, that's kind of relevant to being able to do your job? I'm not trying to pile on to people that have anxiety issues, but being able to do things under pressure is a skill. If we're up against a deadline and you entirely freeze up and can't do anything, that would be a bit of a problem wouldn't it?