It's not an issue of spreading the virus or lung damage. Hospitalized patients are often intubation. Long term intubation leads to cognative dysfunction and multiple system and organ damage. Also, recovered patients not intubated are showing signs of cognative damage. Along with unknown residual long term health issues post infection, conservatively better to disqualify.
I'm sure the FAA will have a special issuance medical protocol as well. That would not be a good thing for us.