I agree with the parent that take home projects (as the initial filter) are a non-starter. It's because they're flat out abusive. The employer uses their position to offload the cost of their hiring onto job seekers. The fact that our first interaction is exploitative couldn't be a bigger red flag.
However I am completely fine with fizzbuzz tests, even take home fizzbuzz. But this literally needs to be something that will take no more than 10 minutes, and for most people a couple of minutes tops. And in the question have a disclaimer: if this takes you more than 10 minutes to do, this won't be a good fit, so save yourself the trouble.
I actually don't mind the idea of take home projects, but only after significant investment on the part of the company. They need to have something on the line as well if I'm to devote significant time to it. Paying a good hourly rate for the time to complete it is the most straightforward way.