I can either think OR talk, I can't do both at the same time. I can happily think and THEN talk but when I've interviewed with companies that have this interview culture (i.e. Google) they don't let you do this. They start telling you they want to hear what you're thinking. Also, most of the time thinking is disjointed and nonsensical and is way faster than what you can express so it's actually disrupting the problem solving. I really don't understand what's wrong with letting people think for a few minutes.
Additionally I am perfectly fluent in English and talk code everyday in English but it's not my mother tongue so having me chit-chat my thinking away while I think (potentially in another language) hinders me since I focus more on what I am saying than actually solving the problem.
>> "My typical work process in a technical challenge like this is to spend a minute or two thinking quietly about the problem and writing down notes, I’ll share those thoughts with you in a moment to get your input"
That's great, but that hasn't been my experience. Interviewers constantly tell you to talk and it's specially bad during a phone interview. I'd be fine if the interview was really setup as a collaboration between two people, but it's not, you're given a problem and a whiteboard.