Interesting article, Benjamin, you're raising some very valid points, but I think the conclusion is wrong — it shouldn't be "reject all take-home assignments" but "Be careful with them", as almost nothing is black and white
1. Portfolio: some of the designers just don't have proper pieces to demonstrate their skills (due to NDA or the project is horrible despite of their best effort or something else). Whether to show their skills they'll do yet another Netflix redesign, or actually think about existing product problem, should be up to them to decide.
Plus, with all the "how to create a case study without work experience" portfolios it's no surprise you can't trust some of them.
2. Take home assignment shows how the candidate approaches research and thinking outside of 1 hour.
Yes, design is collaborative work, but some of us (i.e. introverts) do our best/deep work outside of the group setting of the whiteboard challenge. What share of your time you work on your own and what share do you spend in the white-boarding setup?
Whiteboard exercise also gives less insight into how a person approaches UI details
Having said that it's hard for the companies not to be biased for candidates who put in more hours ("looks how motivated are they") but the solution to it is a) see how can you enforce time restrictions b) be precise about what you're assessing
P.S. assessing hard design skills is not that different from assessing developers: designchallenge.io