It's not like you forego the in-person interview and don't learn what you can from that. The point is, by including a take-home portion of the technical interview you can get a better sense of the individual's technical abilities.
If, in addition to what seems to be a technically competent individual, you find they don't perform well in-person, then you take that data and weigh it against where your priorities lie for the position.
There's a huge difference in knowing "technically great, performs poorly with an audience" vs. "technically poor, but we only tested them with an audience".
Furthermore, it's not uncommon for people who experience anxiety during the in-person to loosen up as they acclimate to the office environment and their peers. These people can actually be some of the best contributors, and it can be a very costly mistake to misjudge them. This personality type tends to be quite loyal and averse to changing positions, because the whole process of interviewing and acclimating to a new environment is so stressful to them.
You seem to have a chip on your shoulder in this discussion, are you having a bad day?
Not at all, I'm enjoying myself and the debate (while finding it kafkaesque that people are finding ways to defend failing fizzbuzz on an interview). How are you doing today? That might be the only legitimate point I've read in this chain so far - if you hire people too socially impaired to write fizzbuzz, they'll be less likely to job hop.
Now we're tacking on an additional aspect of the job that we didn't know about before. If the job requires a social interaction with people outside of the company then, of course, it becomes a factor. Let's not be silly in an effort to just be right and prove someone else wrong.