If it's important enough, the guest will contact the hotel. It's great when the hotel has taken care of the item. The hotel should NEVER contact the guest, rather, the hotel should err on the side of caution.

Perhaps the guest was having an illicit encounter. Perhaps the guest was on a job interview and the email account is the guest's work email. Perhaps the item was left on purpose, but why should the hotel have to take the time and effort to track the guest down.

I left something very recently at a hotel. It took me two weeks to remember which hotel. The hotel had the item. I sent the hotel a prepaid FedEx label (via email) for the item to be returned. I don't feel slighted that the hotel did not contact me, nor do I expect the hotel to foot the cost of my scatter-brain mistake. I am grateful the hotel kept the item.

When I was in school, I waited tables. Mr. and Mrs. X were regulars, coming in about once a week with their daughter, who was around eighteen. One day, Mr. X left his credit card. He had put his phone number on the receipt, so I called and left him a message that it was at the host stand and either he or Mrs. X could stop by and pick it up. Mrs. X came in to pick it up. Only Mrs. X was NOT the woman we were used to seeing with Mr. X and had assumed was Mrs. X. The woman we assumed was Mrs. X was the mother of Mr. X's daughter, who the real Mrs. X was told had been out of the picture for years. I felt horrible. Mr. X felt it important to be part of his daughter's life. (The daughter was a developmentally disabled adult) and had managed to do this without Mrs. X knowing, as she did not want him involved with the ex-mistress, we later found out. Mrs. X told me in no uncertain terms that she was the real Mrs. X and the other woman was "some tramp" in her words. Mr. X never came back to the restaurant. I felt horrible. Still do to this day.