I guess the challenge in this situation is that the whole reason for take-home work is that introverted interviewees get flustered in person. Won't this happen when the review happens?
This still seems like a better idea than "Tell me about yourself" and "How many golf balls fit in a 747?"
At that point, the candidate should not be hired.
If the candidate can't communicate while writing code, and can't communicate about code already written, at some point you have to be afraid the candidate just can't communicate.
If this is a person who can communicate in any situation except an interview situation, then it's a Catch 22 where their ability to communicate in a work environment just can't be verified.
(Unless you secretly record them communicating in some other work context? Probably not a scalable approach.)
Personally, I think this is where the skill of the interviewer comes in. A skilled interviewer can bust through bullshit fairly quickly. A big problem in interviewing and hiring right now is that most of the interviewers are not skilled. Thus, companies try to come up with processes and metrics that (theoretically) remove the interviewer skill from the equation. Unfortunately, this seems to be done in a horribly unscientific manner.