Your robot package cabinets are more or less exactly what Amazon has deployed as "Amazon Lockers" [1] at least in the Seattle area. It works remarkably well for normal-sized packages. They are popular enough in "walkable" parts of the city that some of them are routinely full.

Shortsighted placement has occasionally put them in shopping mall interiors that are not 24/7, despite having a 24/7 grocery store in the complex... Hopefully these issues will be ironed out in time.

[1] http://goo.gl/fZNqmH <-- Links to Amazon.com