Maybe it could have an alarm and real-time video that is sent directly to the police?
Real-time audio and video might be very bandwidth (and therefore battery) intensive to transmit over a cellular connection. Instead, it might be more efficient to include a heartbeat signal that transmits the last GPS coordinates, and maybe a static image transmitted every second. When you stop receiving the heartbeat, that indicates that the robot's battery died or it is in trouble.
In this hypothetical future, our online culture would mature. I do not see when we would send a robot when things could get to us. Just doesn't make sense to me
We already have mail delivery systems, which scale pretty well AND can be augmented by bots and other technological advances. I have a hard time seeing how your claim holds besides some corner cases like "need fresh tomatoes for cooking in this evening".
Similar to how there are smaller stores that don't accept credit cards yet, most shops probably won't support any sort of delivery either. This is already being addressed by services like doordash/grubhub/postmates/etc, but it'd be cool to have your own personal doordasher that you (presumably) could pay normal store prices with.
I do think the more likely scenario though would be somebody like doordash firing their human delivery drivers and just having robots/drones do it instead though.
An autonomous robot suitable for generic (or even a few select) tasks is rather complicated and/or requires non-trivial infrastructure at the site of service (e.g. grocery store).
For example a carrier bot following the delivery person is much simpler in comparison and can increase the efficiency of the mail delivery system without putting new infrastructure in place everywhere. With standardized mail slots some deliveries could even be automated (still less complex than a robot at every shop the fills up your robot or your robot having picker capabilities; plus your robot might need your car to get around).