I think these things are tools and it depends on how they are used. A big problem is that people use these tests like exams… but they don’t know how to write good exam questions, and maybe don’t know how hard it is to evaluate someone. Writing a simple methodology for a science experiment is hard enough, let alone evaluating a human.
Secondly people don’t actually know what they want to hear from a test. I’ve sometimes asked questions in an interview about the test and afterwards received feedback that I was aggressive and shouldn’t have questioned the interviewer. This suggests to me a couple of things - that they didn’t know what they wanted from the exercise, that they couldn’t answer questions about their own exercise because they didn’t understand it themselves, and that they have a culture where asking for answers from authority is frowned upon. In a way, it worked - they didn’t want me and I didn’t want them. My biggest piece of advice in using anything for an interview is to understand it, understand the context around it, and know what you’re trying to learn by doing it. If your plan is “give them a puzzle, watch them, then judge them” then you’re wasting your time and theirs. If your plan is “give them a puzzle and add up the marks based on their performance” you’re either a professional assessor or you’re wasting your time and theirs (or both).
Do you know what’s a puzzle and reasoning test at the same time? Software testing. Get candidates to test something and rather than judge them by what they find (after all, who is ever, in real life, expected to find all the interesting problems with a brand new test item in a brand new context in an hour?) ask them to explain their process and thinking. Make it obvious that saying “I don’t know what I’ll find out” is okay. The problem with testing is that an amateur and a skilled professional both look like people sitting in front of a computer with a blank expression on their face. One is inner thought and structure and careful application of heuristics and evaluation of methods and so on, the other is someone banging on it randomly until it does something. So to make that tacit information available you have to get them to test something and try to express their inner process to you. Oh, and you’re not seeing how well they do on their own, but trying to get them to do their best to see what they could be capable of. If your interview is “how well does this person perform when they’re very nervous around new people and in need of a job with no encouragement from me” then you haven’t seen what they might do if you put them in your company. Get them to communicate their findings - their testing story - including what might make it more testable or what they’d do with more time and resources. Make it clear that questions are fantastic and keep reminding them to ask questions - you don’t want to say “well, they didn’t ask any questions” - you want them to ask questions and then question the questions (“Does the answer to your question matter? Why does it matter?”).