Imagine if the virus doesn't have a fatality rate that's very high in one sense, but it's high enough to overload the healthcare system so that most people who need to be hospitalized will just be left to die for a few months.
It won't end civilization, it won't be a blip in population growth, but I have a very strong reaction that "pride goeth before a fall" and you shouldn't go and assume that you and everyone you love will be lucky. It wouldn't make sense to destroy civilization or the global economy, but I don't think it's obvious that coping efforts are not worth a few trillion dollars in redistributed wealth and a lot of "nonessential" people staying at home for a while.
From some of the charts and numbers I've seen, about 10 million people in the world die from infectious diseases in an average year. If everyone got COVID-19 and 1% died, that would be something like 70 million. Plus who know how many would die from other causes that could not be treated due to the epidemic. So, what is worth doing to save 70 million people? I don't even know if I want to attempt to answer that, but if you're saying we're going too far, then you should have an answer.
But whatever, I'll attempt to answer myself. In the US, my impression is that liability for a death in civil court, could be on the order of a million dollars, as that's the order of magnitude of what an average person makes in a lifetime. Multiply a million times 70 million and you get $70 trillion. So that puts bailouts and stuff that cost a couple trillion in perspective. Maybe it is in fact coldly rational to try to prevent the virus from spreading?