The "two weeks" originated from the idea of instituting periodic, local lockdowns in order to keep hospitals from filling to overflow. The idea wasn't to keep people from dying from COVID-19, per se. The idea was that there would be some people who would be affected severely by the virus, but who could pull through if given supportive care in a hospital. What we didn't want was numbers getting so high that people who could have pulled through wouldn't because there were no available bed for them. That's the original idea behind how lockdowns were supposed to be used.
But, returning to my original point, once things locked down, a number of politicians realized that they would be blamed for any deaths that occurred when the lockdown was lifted. These politicians received support from the "if we can save even just one life" crowd — which I'm characterizing as the neurotic.