As someone who appreciates empathy… the way I see it is that it’s not about you. It’s about the people you have potentially exposed unwittingly (remember even in symptomatic cases, you can go several days without showing any symptoms, but still be shedding/spreading the virus).
From a purely selfish standpoint… if you have the virus and get a serious case you want to make sure that you get treatment as soon as possible. This thing isn’t a joke or even “just a flu”.
(I put that in quotes because even flu isn’t “just a flu”. People’s lack of respect for a proper influenza outbreak is part of the reason we’re in this mess. Flu is a killer that deserves every bit of our respect. We’ve honestly been lucky we haven’t been hit with a novel strain of flu that could tear through the human race like the Spanish Flu epidemic of 1918 did.)
In the beginning we thought it was “just” going to be a respiratory virus. Turns out this thing thickens blood, causes bloodclots, which in turn causes strokes and everything else that goes with clots.
So there’s two reasons. One selfish, one empathic.