It's a bit more nuanced than that. For example people proven to have been already infected can reduce distancing. Some distancing measures vs baseline can be left in place permanently (e.g mask wearing).
It could be theoretically possible to reduce distancing between immune persons. However this creates
1) a social and economic pressure to also get infected and ignore the risks
2) a control problem: Suddenly, many people are outside and socialize. How should the police differ between the two kinds?
3) even after the symptoms have gone away, the virus is still contained, e.g., in the stool. So you would need vast and repeated testing to check who is not infectious and immune.
