Have you done this? My worry would be that sooner or later you'll have a candidate who posts the assignment online ruining your weeks of effort. It also seems like it makes it much easier to cheat if you make it a take home.
I'm religious about this topic for a reason. :)
No, I attribute the turnover to the recruiting mechanism. We found great people who were sorely mispriced by the market, and we took advantage of that to create a win-win scenario: people without the resume to get a similar job at a competing firm got an extremely impactful resume bullet and a good-paying job, and we got people who genuinely wanted to be on our team and weren't applying as a once-a-year lateral job-hopping gamble.
(I have no problem with people job-hopping, by the way, but every employer is trying to minimize their exposure to that.)