That's why I think that a paid take home test is the best way to understand how someone can program.
But the job of an interviewer is to get data any way they can, and the job of the interviewee is to provide that data as best they can. For the interviewee that means it is almost impossible to over communicate what you are thinking when faced with a problem. (I know, it's not easy to do, I have been there.) It's not natural or what you do when you are programming typically, but an interview is not a natural environment, nor should it be.
If day to day coding in your company generates my interview level of anxiety and stress then you are 100% right that I would not be a good fit and you are doing me a favour by not hiring me.
The problem is that some people don't realise just how stressful interviews can be due to them not suffering that level of stress, anxiety etc. so it's difficult for them to see themselves in that position.
I wish every hiring manager had that experience as it gave me a lot of empathy for candidates.
Even pressure comes in many forms. When your future and career is on the line and you're being judged by a bunch of strangers, it can feel very very adversarial. Instead of having the interviewer's trust, you have the anxiety that comes from the mere thought that they're looking out for all your mistakes and failures. They're doubting you, out to get you. (Even if they weren't, that's how many people often feel)
By contrast, you can have immense pressure in production when shit is on fire and you got a sudden unexpected hard deadline and your team & customer is relying on you. How this feels depends on many factors but it can definitely feel more like being a comrade in battle (and the hero of the day). It can even be energizing. Usually, you have the team's trust and support here. It might be stressful as heck, yet the total opposite of adversarial.
It's kind of a big deal. I would never want to work in an adversarial environment, I don't think it's healthy for anyone. But a bit of stress here and there can help maintain a good pace and make the work more satisfying.