As it stands, missing packages are not really a police matter for the recipient - recipients don't really have knowledge that a package was stolen per se, since the package never made it to their possession. Amazon could certainly file police reports, but that requires a higher bar of evidence than throw-and-go delivery service provides, and either way it Doesn't Scale (TM).

I'd guess it's more likely the opposite dynamic, where they'll get a bunch of early adopter types to sign up without thinking through the ramifications. And then after the honeymoon period, Amazon will start demanding those users file police reports for missing packages since from their system it now looks much more airtight that the package must have been stolen from the buyer.