Can't speak of others, but when I'm doing interview I never "take points off" for not talking while coding - as long as they're building the answer in the correct direction, that's all I want.
I think "talking while coding" is, at least in theory, for the benefit of the candidate - if they're "thinking aloud" and about to make a mistake which may take 20 minutes to recover, the interviewer can gently nudge them in the correct direction.
It's not about talk while coding. It's about letting your interviewer know what strategy you employ.
I fully expect Sr engineers to talk about why they choose the approach they do, and then implement it. I can adjust their approach while I hear about it, and then let them code it up.
This whole being silent and focus coding is bs I think. When you're doing the typing part, don't talk, just code. When you're doing the strategy part, talk. I want to see how you'll be able to express your strategy to your coworkers when a real actually challenging problem occurs.
Also. Algo problems are worthless. They only tell me you know how to cram. Don't do those, they don't actually answer anything. If I see that in an interview that's a flag for me that their eng culture might have issues. Only exception would be if you're applying to a job where you'll be doing that all day.
I think "talking while coding" is, at least in theory, for the benefit of the candidate - if they're "thinking aloud" and about to make a mistake which may take 20 minutes to recover, the interviewer can gently nudge them in the correct direction.