To be frank, if I were the ruler of the universe, I would have charged people for the first rounds of the vaccines when waiting list for the vaccines were long. I would even go as far as to declare that insurance companies could not pay for the vaccine.
This would have had two positive effects: It would have raised funds for the health care system (without having to raise taxes), and it would have made the vaccine appear to the world as something valuable.
For the second rounds of the vaccine, I would have created mechanisms to "waive the fee." The waiving of the fee would have been a sufficient inducement for most people.
Providing all of the vaccines for free made a false economy and de-incentivized vaccination.