But for your first point, that wouldn't seem to make much sense given the time investment from the company as well. It takes time to review take home tests, much more time than it takes to review a resume or even for a recruiter to have a quick phone call with the candidate. So why would they send out a test to someone first?
I've usually seen something more like this, which I think generally works fairly well:
1. Initial resume screening 2. Quick phone call with the recruiter 3. Usually some kind of technical call/interview with developer(s), engineering manager or similar, at the very least some discussion of experience and background 4. Send out the test, review it, call the candidate back in to discuss if they want to 5. Probably some other stage at the end
For example, it's very tempting for a company to send out tests before doing much resume screening. Why should I spend 30 seconds looking at a resume when I could have the candidate spend an hour on a test, and save myself 30 seconds?
Or what if I set a take-home test which is supposed to take 1 hour, but also supposed to really to stretch candidates' ability and give the best candidates a chance to shine? Probably a lot of average candidates will give themselves a bit of extra time - and before you know it, I'm sending a "1 hour" test that takes an average of 4 hours.
Take-home tests are a lot less objectionable if you can properly guard against these problems.