I'm kind of split on these "vaccine lotteries".
On one hand, they're a gratuitous waste of taxpayers money. by bribing the populace.
On the other hand, studies show that those who are hesitant can be swayed... psychological studies on overestimating rewards and all that ... so if it gets more people to get vaccinated quicker, and then rejoin the workforce; the benefits offset the seemingly frivolous expenditure.
The older I get, the more I realize that you have to accept cognitive biases, like the ones at play here, and just use them to get what you want.
Of course, anyone moderately intelligent looks at something like this as being completely dumb.
You are also no Thomas Jefferson or Thomas Paine.