Whether the state is wealthy or not, I don't think taxpayers (everyone) are thrilled with such spending. And even though most people are reasonable (we will assume that this is so), there are people who, in pursuit of a ghostly chance to win a prize, will make decisions that they would not have made without this option.
The amount is not that big. Ohio is a state with population of 12 million. Two doses of the Pfizer vaccine to each citizen is going to cost the state government some $900 million. Then there are additional expenses from logistics and arrangement. The justification from the state government is that giving out $1 million in school or college scholarship is OK, if it prevents the wastage of tens of millions of USD worth of vaccines. Pfizer vaccines have limited shelf life, and they need to be stored at -70 degrees.
I understand that in terms of the state budget or in relation to the total cost of vaccination, this is an insignificant amount, but in natural numbers it is still significant and despite the planned savings in vaccines, this method of luring the population to vaccination seems immoral and unacceptable to me.