I think with most jobs, they know you have the skills and experience or you don't even make it to the interview. So the interview is more about whether you are a cultural fit, whether the way you make decisions aligns with the organization or department, etc. For highly technical positions that are only technical positions, sure, a test of some kind might be better. But even then, you could easily end up with a guy like the letter writer, and that's the entire point. That guy may be a great programmer, but he'd still be a nightmare employee. I think his entire situation shows exactly why interviews are valuable and not badly flawed. They did exactly what they are supposed to --weed out a guy with the experience and technical skills, but that you still most definitely don't want to hire.
Even a 3 week trial may not bring to light that this guy is a nightmare. During that time, if he doesn't need to be corrected, directed, or have his work scrutinized, everything may seem fine. If no one sees a way better than his and tries to tell him that, all seems well. So the interview found what a 3 week trial likely wouldn't.
Probably the best option would be to have both, but these trial periods would be nightmares for employees. Certainly you couldn't secure a new job while still working your old one. And you would also have to pause your search, do the trial, and then continue your search if that fell through.
These posts lead to a nice conversation last night with DH during our dog walk. He's beginning a job search and starting to prepare for interviews. I asked him this question to see if he had an answer, then I told him about the AAM letter and resulting conversation.
His answer is basically the same for the "biggest mistake" and "biggest weakness" questions, with one having more details about a single specific incident. We talked about how his answer shouldn't just be the mistake or the weakness, but also that he's aware of the issue and therefore takes steps to mitigate it. So it does show how he thinks, but also that he's self-aware and knows how to manage this area of weakness. Sure, some employer could be like, "yeah, we can't have a guy with a tendency to do X as that's not a fit for us", but mostly, they will [hopefully], think, yes, this shows us he learns from his mistakes, is thoughtful about balancing some instincts that are useful in some cases but not-great in others, and he can be managed effectively."