In the book Systems of Survival by Jane Jacobs, she makes the case that there are two main systems of ethics that the world operates on. She labels these Guardian and Trade.
Caveats: These systems are not intended to be exhaustive systems of ethics, but only to show the features that distinguish the two. And I won't be doing the complete thing here. If you want more, please read the book.
The Trade system is appropriate to people getting their living by making stuff and trading goods and services. The archetype is a store keeper. This system contains things like openness to innovation, optimism, industriousness, etc.
At the top of the Trade list is Shun Force. This is primary because introducing force into a trade will, at best, distort the trade away from win-win. At worst it becomes something like mugging or piracy or a protection racket or something of that nature.
The Guardian system is appropriate to people getting their living by getting and holding control of territory. That is to say, most forms of government and associated features. It contains things like loyalty, honor, prowess, ostentation, and being fatalistic.
At the top of the Guardian system is Shun Trade. This is because the Guardian must wield force as part of his job. The Guardian is the soldier, the police officer, the border guard, etc. For a Guardian to participate in trade as part of his job is, at best, suspect. If you are tasked to guard a territory, and you start trading it away, the best that people will think of you is that you are a bad guard and that you are flirting with treason.
Rather than trade, Guardians are directed to use largesse, which is a very different thing. Not simple charity, but rather, as reward for and inducement to loyalty. The Roman soldier who came home victorious got rewarded with land. The political guy who helps bring an election victory winds up with a cabinet post.
Each system is shown to be self reinforcing. If you follow all the precepts of the system appropriate to your job, you come out being respected and doing a good job. If you fail at some of them, you wind up failing at your task. Think of a shop keeper who carried a gun and used it as part of his shop-keeping. Think of a soldier who was constantly trying to bargain away the territory he was to guard.
The book deals with many cases where people have improperly followed the precepts of the side they were supposedly on, or that mixed the two sides. Police given quotas and rewards for lots of arrests, and they wind up inventing reasons to arrest innocent people. The Mafia being incredibly industrious and hard working (a Trade side virtue) but using it to control territory (a Guardian side virtue). And several other examples. Staying to your side works. Straying outside rapidly causes huge problems, and quickly after that disasters.
What is the relevance?
Government wields force. That's necessary since they control the territory. Value neutral here. Not saying they are moral or not moral to do so. Just that they in fact do so. They are Guardians. So they have a huge tendency to look at those who follow the Trade path as suspect and contaminated. Successful governments have an incredibly strong tendency to see free market (that is, for profit) activity as automatically tainted with disloyalty. In the mind of a Guardian, the calculation goes like so. If they were loyal they would be doing it to benefit the government, not to make money. The examples of people who "sold out" and betrayed their home territory are so numerous as to be cliche. And Guardians revile them all very intensely.
So governments see COVID-19 vaccines as something to be given to those who have been loyal, or that it would be valuable to encourage them to be loyal. This is why, for example, some politicians have floated suggestions that certain political divisions should get vaccines first, completely differently from those who have the most urgent medical need. They are trying to reward loyalty, and encourage others to be loyal.
So it is only natural that governments don't want any distribution of vaccines outside of government controlled channels. For-profit activities are seen as suspect, and they want to do it on largesse. And the efficiency of distribution is only a very minor, very low priority consideration for them.