Illnesses and accidents are exactly the things you need savings for, and aren't really relevant here because they don't prevent you from saving until and after they happen. The issue appears to be that 50% of Americans live paycheck-to-paycheck and have no savings? I can't imagine how this could be anything other than them just spending money on shit they don't need.
And yes, I am assuming you live in a developed country. I have Ukranian citizenship and right now the Ukrainian government is abducting men who are over 24 years old and sends them to death. If you live in a country like that, true, you shouldn't worry about investing because you don't even have basic human rights.