Problem is solved before the solution is consciously perceived. The reverberations after perception can be of many different styles.
There is little value in chain of thought and I think humans are implicitly or explicitly instructed to verbally think and hinder their problem solving facilities. There are many examples of individuals that went much further with their own internal but externally indecipherable thinking models because they avoided language as a thinking faculty.
On top of that to ask for clear communication and decoding of the verbal thinking mush into sounds is just an extra hinderance. Id prefer to ask questions to evaluate understanding of the problem solved than force someone to dump their mush into a clear spoken summary.
Interviewing process is just a mush of nonscientific nonsense , a theatre for all involved, a sad affair.