I don’t think I think so differently from you and managed through a few interviews with success. I almost go further than the OP by suggesting to interviewees that I have a blank page of notes I need to fill in with evidence to support hiring them, for someone else to read. The coding question is to kick start that process.

The thinking gives more than just the answer and makes it more of a conversation. As a candidate I will mention projects I had similar when think about anything. As the interviewer it is hard to gather experience: so many people stay abstract and it’s infuriating (let me help you get this job! Yes you can do something means nothing; when you did do something means everything.)

I am sure that many interviewers don’t see it like this however and treat it like a quiz sadly. Best advice for interviews I was given as a candidate: the interviewer will decide in the first five minutes if they want to hire you. The rest of interview is them trying to convince themselves and others of that decision.