First let me admit that this is mostly based on comparing modern times to movies, tv shows, novels, etc from the 1940s & 50s; as well some rudimentary knowledge of Los Angeles history of that era. (If you’re looking for a good story go look into Harry Raymond. Private eye who survived the bombing of his car by an LAPD police detective) For all I know there could be more people employed as private detectives then ever before. But it certainly seems like the job is far less in the public eye then it was in the past. Might the rise of no fault divorce have anything to do with it? If you can just leave your cheating spouse there’s no need to hire someone to get evidence for a judge.
I covered the decline of one particular brand of private eye, the hotel detective, in an earlier answer, and certainly that decline was in significant part caused by changes in moral norms. While you're waiting for fresh – and hopefully broader – responses to your query, you might like to check out that response: