Note that I said Fizzbuzz, not an actual in-depth programming question.
FizzBuzz (and similar) questions tell me nothing whatsoever about your programming ability, but they can tell me everything about your lack of it.
In the limited time I want to spend interviewing, an hour on FizzBuzz is a massive waste of everyone's time.
I agree entirely that it doesn't prove anything about a candidate's likely success as a hire, but it is a reasonably strong signal about their likely failure.
When I experienced FizzBuzz as a candidate I was coding onto a projected screen, and the test involved writing unit tests and doing a final refactoring step into something "reusable". It took the best part of an hour. The instructions themselves required a good 5-10 minutes of reading/parsing to understand exactly what was expected of you.
If it takes a candidate an hour, something is wrong.
How could it possibly take an hour to write fizzbuzz for anyone of reasonable ability?