I once left my house keys in a Paris hotel. The hotel contacted my travel agent who then contacted me. I was so grateful (although I had also realised where they must be) and managed to get back to the hotel to collect my keys before my flight.

I do think that for exceptional/valuable items, the hotel should contact you. Although how they are meant to do that if they have your phone is a bit perplexing - but keys/wallets/passports/laptops/phones - yes, they should.