going through a long sickness usually leaves one weaker afterward, even if one is cured, no? and in some cases there might be a slight upside in acquiring a certain degree of protection from future illnesses from that disease through various immunity mechanisms (which are of course far from perfect).
Okay, yes, that's one way the analogy breaks down.
It's more like you always had a disease and just didn't know it. Celiac comes to mind as a common example. I know people who improved a lot once they got diagnosed, and just never realized the symptoms meant anything before that.