In something like administering naloxone or I suppose CPR training, or even just educating people about the Heimlich Maneuver, it seems like a key contributor is that an immediate response by someone on the scene of an emergency is critical. The expectation is "if you happen to encounter such an emergency, you're now able to do something to help". What you're suggesting seems qualitatively different -- proactively sending out non-healthcare-providers to administer something to people before they get sick.
And yet, if we want to administer it to billions of people quickly, maybe that will be necessary. I also wonder if that will be the bottleneck, or if producing/distributing everywhere it will be.
This vaccine has not been tested in chimpanzees (and actually such experiments would probably be a challenge, since they may have existing immunity to the backbone adenovirus).
(edit: parent comment initially mentioned experiments in chimpanzees rather than mice)