Right, say I buy this test and find out that I've already had, and recovered from, Covid-19.
Now that should mean that I'm OK to go out and resume my normal life, safe in the knowledge that I couldn't catch it, wasn't incubating it, and was not infectious to anyone I came into contact with.
But how would other people know that? If I breezed past someone in the supermarket, sat down next to someone on the tube, or booked a GP appointment, how would others be able to tell that I'm "safe" and they have nothing to fear from me?