I think where you live will determine what or how much you should “stockpile”. I could simply call a medical info line if I were worried about being sick, or go to a clinic or hospital (walking distance) if sick with zero worries about $, I live in an area that is the opposite of a food desert (walking distance to 6 - 7 grocery stores), have friends and family close by, am not vulnerable health wise, my cupboards are filled with basic foodstuffs. In any case, I live in a 3 and a 1/2, not sure where I could store big quantities of food.
Of course I’m not panicking, it’s easy for me. Not everyone is in the same situation. I would think that thinking ahead, “stockpiling” If I were far from resources, or had medical issues, would be the exact thing to do to keep my stress levels down. Being prepared makes you less likely to panic.
I’ve seen some pics on Twitter of empty store shelves and such and just assumed they were from places where there was only one grocery store, because otherwise, that would be strange.