Yes, writers who can deliver correct solutions as consistently as Ellery Queen or Agatha Christie are rare indeed. Hollywood has more or less solved that problem by decreeing that since the world doesn't make sense, movies and television don't have to either. Jane's feats are about as well rationalized as Sherlock Holmes' I think. Most of the time pretty well, particularly as the writers do know that most people remember only the successes, but with the occasional glaring lapse.
For my part, the key to Jane's appeal is that his mean streak is aimed largely at worthy targets, and otherwise more or less under control. I could believe the medical examiner turning to him, for instance.