Thinking about this some more, I don't think the nominal mechanism of government matters.

It's a split between extirpate the disease and minimize the cost ("re-open as soon as possible", etc. All the approaches trying to return everything to normal as quickly as possible.)

Minimize the cost is a mistake; it's an approach that axiomatically supposes there's a finite quantity of disease. (There's a lot else wrong with it, but that's the fundamental and unrecoverable error.)

So the question might be, "what's the difference in thinking that leads to extirpate the disease versus minimize the cost?"