Would this carrot and stick approach work to get more people vaccinated against Covid?

The carrot: A cash payment when you get the shot.
The stick: A special fee added to your bill if you become positive and need medical attention to cover some of the extra costs involved. Fee would be waived if you were vaccinated.

As an example:
The carrot: $ 100 Covid Vaccine incentive Payment to everyone who takes the time out of their day to schedule and get the shot.
The stick: A $ 300 Covid Cleaning and Convenience Fee added to your medical bill if you are diagnosed with Covid. (Waived if you have been vaccinated)

Now let’s estimate what the payment and fee should be and see if these numbers are reasonable.
First we need to determine the cost of Covid on society.
I’m sure CDC has these numbers but let’s make some assumptions and approximate the costs per person. (Feel free to make your own estimates and correct me if my numbers are way off. I made a spread sheet and can fix it in a second.)
Assume 30% of people would eventually get Covid and lose 1 day of work. Assume 50% are working. At $20/ hr = $160 x .30×0.5 = $24 per person
Assume 10% of those who get it, go to the doctor. At $200 per visit. Cost = $200 x .3 x .10 = $6 per person
Assume 2% of those who get it are hospitalized for 2 days, At $3000 per day estimate = 6000 x .3 x .02 = $36
Assume 0.5% of those who get it die. Life worth $300,000. Cost =300000 x .3 x .005 = $450 per person
Total cost per person= $24 +$6 + $36 + $450 = $516
Assume 25% of people at medical office will refuse vaccine need to pay fee. $300 x 0.3×0.5 = $2.25 per person.

Total cost of Covid in the US = $516 x 330 million people in US = $225 Billion The number is much, much higher in the trillions but let’s stick with this for now.
Cost of $100 Vaccine Incentive payment (carrot) for all US = $100 x 330 million = $33 Billion
Income from Covid Cleaning Fee = 0.7 Billion (Ignore it for now).

It seems we save $225 billion by spending $33 billion. That is 5 to 1 I’m just an engineer with a calculator but this seems like an obvious choice.
I know vaccines are not perfect. I’m sure I missed some things. Please correct me and tell me what I missed.

If you were on the fence or not planning to get the vaccine would you get it if this program was in place?