I think if someone's in a higher risk group, or they regularly visit someone in a higher risk group, and *if* the body holds immunity to the virus for some time (a year or so at least) then if someone knows for sure they have had it, maybe they can worry less about going out or visiting their relative if they're not going to come down with it now (as they've already had it) and once recovered they're a safer person to visit the relative or they could be the person who takes food and water into the room of a person in their household who gets it in a few weeks or months?
That's the main reason I think it might be helpful to know for sure who's had it and who hasn't.