I think you are kidding yourself if you think the majority of these companies are satisfied with an answer consisting of "This looks like it's beyond my skillset". All things considered, they are going to progress the candidate who can solve the problem because it's an early stage test.

I wouldn't feel pressure if my mom threw me the problem, but I still probably wouldn't be able to come up with a solution (or even approach anything useful in a reasonable amount of time) that would satisfy an interviewer because frankly, I'm terrible at it and haven't spent the time to get good, just like many, many other successful developers.

Stress is only one aspect of these that people dislike.