In general, I agree with everything except whiteboard challenges. They’re worse than take home tests! Nobody normally codes under that type of pressure, and they are nothing like writing real code. They don’t allow you to design bottom-up, or think in a way that your brain works.
The take home tests that seem to work well are short (a few hours), open-ended ones with some direction. It allows for creativity and less pressure since you can work on it any time. Taking notes shows a person’s thought process, and the final code shows their ability to create abstractions, organize code, and work under a (soft) deadline.
I use my subconscious to solve problems, and that means thoughts don’t bubble up immediately. They may take a few minutes or hours, and that doesn’t really work for whiteboard tests. We’re not air traffic controllers that need to make split second decisions. Software would be disastrous if that were the case.
Of course, I’ve also seen bad ones. Too long (> 8 hours), or too detailed (make a clone of X). As a bonus to working on take home tests, you own the code and can show it in other interviews. If it’s not working, take the time to fix it and add your own creative aspects. If you haven’t worked on any personal open-source projects, this is your jump-start.