I have been on the receiving end of applying to an agency and being told I didn't make the grade technically. I was disappointed because I know I am a good engineer but I didn't expect them to magically know this. I can also see how my approach to the technical tests might have made me look less than what they were looking for, which is fine.
I am also not sure of any good alternatives because someone will always object to any alternative which they cannot achieve for some reason. A "take home" project is good for real life work but some people cannot (or will not) invest the time even if they are paid for it; discussions can be great for helping nervous people but that is not how work usually is, there are challenges, pressures etc. and the able people object that it is not fair that people are getting in too easily.