If governments do absolutely nothing, the economy will shut down on it's own through reduction of consumer demand, stalling of business investment, massive employee absenteeism, and a destroyed healthcare infrastructure.

Governments are just trying to coordinate and expedite the shutdown. We won't know if that made a difference for a long time, to your point, but the economy was going down regardless IMO. This isn't a choice of lives vs economy; it's just a really crappy virus.