Because if reinfection so close to recovery were possible, it would make this virus really unique, and it doesn't really fit the available data very well. It makes much more sense that the virus takes a long time to clear after symptoms abate, and the tests have a really lousy false negative rate.
Moreover, if a lot of Covid infections are in the area and the virus is mutating quickly, a person might be exposed to a different strain soon after recovery and wind up infected, if the SAR-COV-19 is similar to the common cold. This would be hard to notice, since it would tend to happen as the virus was spreading rapidly anyway. It would become a problem only if people expected the virus to abate once everyone had been exposed.
See: https://www.technologynetworks.com/immunology/news/why-dont-...
This kind of speculation is relevant to the more irresponsible approaches; "developing herd immunity" and "immunity certificates" but it mostly should be a reminder to "don't do that because you really don't know what you're getting into".
This would explain: NYC vs LA vs Italy. Why isn't this theory brought up more?
"Wang, whose full name has not been disclosed for privacy reasons, is one of more than 100 reported cases of Chinese patients who have been released from hospitals as survivors of the new coronavirus — only to test positive for it a second time in the bewildering math of this mysterious illness."
https://www.latimes.com/world-nation/story/2020-03-13/china-...