I had never actually thought of detectives as a competitor for the reader, though it makes sense. It explains the appeal.

I took a way more cynical and Doylian angle. I always attributed the (overpowered, uber-competent, quirky) detective to the serial nature of mystery series: they're easy to mass produce if your central character has the same weird schtick for decades and you don't have to worry about scaring away new readers that accidently pick up Book 6 in a series instead of Book 1, because it's the same basic structure every darn time.