Getting the virus does not make you more immune than getting the vaccine.
The vaccine gives you a titer of 4000 (antibodies) than does getting the virus, which gives you around 600 which only last around 4 months. I have gotten my antibodies tested 6 months from being vaccinated and still have a titer of about 3400 and 86.5% immunity.
https://www.cdc.gov/coronavirus/2019-ncov/science/science-briefs/vaccine-induced-immunity.html
People have gotten sick from COVID19 more than once and many have died from the second bout.