Plus having an immunity to one coronavirus doesn’t automatically buy you an immunity to another strain of coronavirus. We are already seeing several new strains.
Also having COVID-19 doesn’t automatically mean your body even develops an immunity. All sorts of caveats might prevent that from happening such as the infection being too mild to begin with (eg viral load).
And lastly, while on the topic of viral load, if your reinfection it too severe then you can still die from a reinfection even if you do have a immunity (immunity gives your body the resistance to fight it, but that doesn’t mean you’re invulnerable to the decease).
So while your points are valid, that doesn’t mean anyone who’s caught COVID-19 and recovered should be thinking they’re bullet proof (metaphorically speaking). At best, they could still be carriers. At worst they could still find their body unable to fight off any new infections.
This is plain wrong. Natural immunity for SARS-COV-1 was observed even 10 years after infection in some trials. Immunity against other coronaviruses also lasts longer than 2-3 months and actually there is strong indication that natural T-Cell immunity might last people much much longer and be sufficient on its own like it is also with other coronaviruses.
The only thing which is estimated to disappear after 3-6 months are antibodies in your bloodstream.