I think my story is the same as many reluctant people: I had Covid, at the very beginning of the pandemic. It was like a flu but I lost my sense of smell for several months.
Having Covid made me question whether or not I should get the vaccine. My body did fight the real disease, why should I inject myself with something that only tries to mimic the real disease? I started to do some research...
My current conclusion is that my immune system is better than that of any vaccinated person who has not contracted the actual virus.
If serology testing can show you have immunity, I would support giving seropositive people the equivalent of a vaccine passport, if the epidemiologists confirm its good immunity. So, I can see a basis for your reasoning.
I would personally choose to still get vaccinated in your situation.
Because the certainty around the natural immunity is probably as questionable as the level of immunity from vaccination. Both are subject to epidemiological confirmation.
The potential harm of a re-infection or of infecting others is higher than the personal risk of being vaccinated.
I understand re-infection is something to think about. But infecting others is not an argument, as vaccinated persons can infect as much as unvacinnated ones. This is proven: https://www.youtube.com/watch?v=TKFWGvvlVLI