Which made me wonder — why is that?
Let's start with normal operational procedures (I don't know if this is a public law issue or not). Military assets are not to be used to replace those of civilian enterprises "unless" there is a exigent need that cannot be met by commercial or other governmental resources. Note: I did this type of planning for the U.S. Army during four years of my 20-year military career. I'll give you an example. Here in Washington state we have mountains that people like to climb. When they do that, they can get into trouble — broken limbs, frostbite, etc. In this state we are helicopter deficient, e.g., the city of Seattle doesn't own a helicopter. Helicopters have limits on the altitude that they can climb. A Blackhawk can only climb to around 10,000 feet. The twin rotor Chinook U.S. Army helicopter can climb to 20,000 feet. So, if there is an injury or rescue to be made at higher elevations, there is a company of Chinook helicopters based at Joint Base Louis-McCord and they can assist (based on the needs of the service first) with a rescue. There is no other comparable commercial resource available.
The U.S. Airforce has 223 C-17 cargo aircraft. This is the workhorse cargo-carrying aircraft that replaced the C-141 plane. They could transport vaccines to an airfield/airport anywhere around the world.
Then I did a quick Google Search for commercial assets:
Fedex — 691 aircraft
UPS — 268 aircraft
Airborne Express — 140 aircraft
Amazon — 50 aircraft
Total — 1,150 aircraft in all
Once the plane lands on the ground the cargo of vaccine will need to be delivered to a commercial address. Here is one number for you: Amazon has 20,000 "marked" trailers, plus thousands more delivery vehicles.
I'm wondering what the strategic, tactical or logistical advantage the military gives that cannot be performed just like, if not more efficiently than, these commercial logistical companies. They certainly have the physical capability to do so. "Amazon is set to pass both FedEx and UPS in US package volume, with the company currently delivering 2.5 billion packages per year compared to FedEx's 3 billion and UPS's 4.7 billion."
I think it all boils down to "it sounds neat and sexy to say the United States military will deliver the vaccines." It is the only reason I can come up with.