Saying someone has "a cold" or "the flu" have such deep roots in common use. This is as much a question of linguistics as of medicine or biology.
As such, it carries with it all the fraught aspects of linguistic prescriptivism. Here, I'm thinking particularly about exercises of, and resistance to, authority.
These terms are like "consumption" or "the grippe" or "the flux". They are descriptive & symptomatic, first, foremost, and probably always, to some extent.
I still boggle at how new, still, molecular diagnostics are, and specifically how, out of all recorded history of disease, the COVID-19 pandemic has been unprecedented in the widespread deployment of them, revealing both their power & their limits.