And even if it's paid, it's still a not-insignificant time investment for the applicant. They're probably applying for several gigs and take home assignments would quickly turn into a full time job, and filing the tax paperwork could take more time than the coding.

And finally, assigning a job that would actually get used at a company pushes up the complexity level, the need to understand the context. This would also make me very suspicious about the motives of the company.

In my company, we give a "fizzbuzz" level assignment on the whiteboard (or their own laptop if they prefer). The purpose is to weed out the applicants who can't code at all (makes a surprisingly large portion of applicants). Additionally, we've noticed that the ones who are good programmers will ace these tests.

I don't think that whiteboard assignments or takehome work is a good way to assess how good a programmer is. A 15-30 minute smoke test with a binary result (the applicant can or can not code at all) is good to filter out bad applicants but not to distinguish good from excellent.

It also shows the company is semi interested and not just meeting the consideration requirements before selecting an already chosen candidate.