Is there really?
I understand that for non-fungible, perishable goods such as organs or test samples there might be a need (though a helicopter would do just as well), but when it comes to supplies, it will be significantly cheaper to just make more of them and stock up on them at each hospital rather than moving them back & forth (not to mention that this particular trial only ranged for 40 miles - this is something a car can easily do).
It won't work unless it's cheaper than the alternatives, and I can't see it being cheaper than just optimizing logistics elsewhere to ensure you have a big enough stock of medical supplies to not need regular drone deliveries (and when you do, a helicopter is an adequate backup plan).