This is, however, slightly unfair. You can't ethically have a rigorous controlled double-blinded study on infection rates of people who have already had SARS-CoV-2. This would require infecting some people with SARS-CoV-2, making others incorrectly think they had been infected, and then letting all of them go about their lives post-"recovery". The ethical problems are obvious.
That said, I'd frankly be fine with letting people with (state-)government-verified past COVID cases act as though they have been vaccinated for a period after recovery (not sure what the period should be). It would be one way to get the next best kind of data (an observational study of vaccinated and recovered patients). It would also incentivize people to get tested (so they get that government-verified past case). I'm not sure it's worth building that bureaucracy, but if that compromise were proposed I'd happily accept.