In the past, when I was a middle-of-the-totem-pole decision maker, we administered a take home. I wasn't really empowered to give feedback, but as far as I know nobody did. The best take home test had a joke in the comments. We were a game company, so it made sense for us - you have to care about entertainment.

Today, as the ultimate decision maker, I ask only to see pre-existing code with git blame turned on, and I review it on screen with the candidate. In this context the candidate receives feedback, and it's almost entirely focused on style because IMO that is the single greatest predictor of actual coding experience.

Let's discuss the underlying issue here: ineligibility, of like 30-50% of candidates. In this context, take homes make sense, because they occur in the absence of any other legitimate reason you should talk to someone.

For example, here are my tech company LinkedIn Talent Solutions screening questions:

Have you completed the following level of education: Bachelor's Degree? What is your level of proficiency in English? During our call, will you be able to share recent source code, wholly authored by you, of a game, application or website you worked on?

Out of 20 candidates, 12 could answer Yes to all three. What exactly should we do with the remaining 8? I can see how a take home can address the ineligibility.