A lot of buildings already do that with packages that are delivered to the front door, I doubt in building neighbors stealing your stuff will be an issue.
Yeah, this. UPS/FedEx/USPS just leave packages in the lobby of non-doorman buildings. People tend to respect other people's packages and security cameras help enforce honesty. In years of living in Manhattan I've only had one package go missing -- turned out that it was stolen by the UPS driver (new iPhone on release day in a Verizon branded box).