My company does take-home interviews (or rather, we give candidates the option to do them; nearly all candidates choose take-home instead of a live coding session) and I don't think I agree with the "lowers the cost to zero" point. First of all, they are never the starting point; we only give a take-home problem to a candidate after we've had an initial discussion with them.
When we get a take-home submission, we essentially run it through our code review process, and as one of the engineers who does reviews, it usually takes me nearly as long to thoroughly examine a homework solution and write up my feedback for internal discussion as it would to do an in-person interview.
Being able to review a candidate's code on my own schedule rather than being yanked from the middle of some knotty problem to go do an interview at a fixed time is a big quality-of-life win for me. But the rate limit isn't much different than it would be with regular interviews.
All that said, it's totally possible our process is super atypical.
When we get a take-home submission, we essentially run it through our code review process, and as one of the engineers who does reviews, it usually takes me nearly as long to thoroughly examine a homework solution and write up my feedback for internal discussion as it would to do an in-person interview.
Being able to review a candidate's code on my own schedule rather than being yanked from the middle of some knotty problem to go do an interview at a fixed time is a big quality-of-life win for me. But the rate limit isn't much different than it would be with regular interviews.
All that said, it's totally possible our process is super atypical.