I don't know about you, but in my work, I always have more than 3 seconds to find a solution. I can slowly think about the problem, sleep on it, read about it, try stuff, think about it while running, etc. I usually do at least some of those for new problems.
Then of course there is a bunch of stuff that is not challenging and for which I can start coding right away.
In an interview, those trick questions will just show you who already has experience with the problem you mentioned and who doesn't. It doesn't say at all (IMO) how good the interviewee is at tackling challenging problem. The question then is: do you want to hire someone who is good at solving challenging problems, or someone who already knows how to solve the one problem you are hiring them for?
You may say "yeah but you just have to think out loud, that's what the interviewer wants". But again that's not how I work. If the interviewer wants to see me design a system, they should watch me read documentation for hours, then think about it while running, and read again, draw a quick thing, etc.
As a sibling puts it though, it's a matter of level. Senior/staff and above? Yeah, that's mostly what you do. Lower than that, then you should be able to mostly trust those upper folks to have seen through the trick.