I agree, the equation changes if you have already caught COVID.
It does indeed. If you have already had COVID that is an even stronger reason to get vaccinated. It may prevent long-haul symptoms, which sometimes appear months after the patient recovers from the initial bout of the disease. It also strengthens immunity.
If you were hospitalized with COVID, and you refuse a vaccination, you are playing Russian Roulette. 10% of patients who were hospitalized die within months of being discharged and going home.