DuckDuckGo follows this process. They in fact do a paid 3 month assignment. May be that's taking it to the extreme and perhaps works very well for them. If I were looking for a job and this process was followed, I'd definitely be game. I will most likely be following a similar procedure while hiring as well. Just come to the office hang out with us for a day - we'll fly you in, put you in a nice hotel + pay you a per diem. All we'll do is work through a problem, not through a series of daunting hypothetical interview questions or some algorithm nonsense that you'll never use in your job.
In some sense many companies do this via 3 month internships. They're basically just low cost future employee vetting opportunities. Of course, they are generally limited to college students.