You seem to treat it as a part of bigger conversation, getting to know how a person thinks, how they solve problems, which may be useful in the whole process. Still, you can reach to answers you are looking without a whiteboard question.
The problem is how interviewers approach the test and if its a component of process that you really need.
The way such tests are conducted matters. Is it a test where a candidate feels observed by at least 10 people from whom majority does not remember how to solve it without googling? What’s the atmosphere in a room? What happened before and after this part of the test? Tech talk is crucial serious part of the interview, but doesn’t have to be humiliating for a candidate to appreciate the job offer. Majority of them did so before even applying.
Plus if you want to understand the way how a person solves the problem, it is crucial to have this person to think aloud. I am afraid that not everybody even bothers about mentioning it to a candidate. Without it you may just suppose and assess on what you see.