Programmers are Artists (Score 2, Interesting)

I think the fundamental justification for a test is that many people in IT (programmers especially) are more artists/craftspeople than professionals. Sure, thinking is a large part of the job, but mental product isn't the sole output (as it is in law, HR, and other professions you mention that don't get tested). Just as you would expect to see work from a carpenter, plumber, or film maker before you hired them, an employer can very reasonably ask you to demonstrate your skills. Just because someone has degrees, certifications, and experience doesn't necessarily mean they have elegance, finesse, or artistry when it comes to writing code or debugging systems. A lot of what the industry values in its employees can't be taught, but it can certainly be tested. Giving a potential hire a code sample with a subtle bug you can judge their process in ways you can't with mere questions. Similarly, asking an interviewee to answer questions on the spot allows them to demonstrate how they code in an ad-hoc environment. This is especially useful for identifying people who don't have enough experience to develop independently.

Also, many professions, such as the law, have certifying authorities (such as the bar) where practitioners must pass a minimum standard in order to join the profession (and can be kicked out of). Because IT has no such standards body, and because so many people in IT are self taught or taught on the job, it's very difficult to know how much someone knows. There is no 'cannon' of IT training, no standard practice, nor even much agreement over what constitutes an adequate body of knowledge. The fact that people with no formal training regularly conceive and develop systems far superior to those with certifications, training and experience continues to speak to this fact.