I would not attribute the requirement of writing out code as something your interviewer personally demanded. He was simply following a template.

The point is that when you write out the code, there will be several other people who will end up looking at it as part of your “packet”. This can actually be beneficial for the interviewee: if you use some technique or library that the inexperienced interviewer has never seen, they might be confused and write negative feedback, but someone down the line will be able to see what you wrote and say, “Oh, this is actually really good.”