The problem with that strategy is that some percentage of the people who become sick need acute care or they will die, and acute care is effectively a fixed res

The problem with that strategy is that some percentage of the people who become sick need acute care or they will die, and acute care is effectively a fixed resource over short time frames. There are a limited number of hospital beds, ventilators, nurses, doctors, and support staff available. The disease can spread much faster than you can increase any of these resources. If you run out of hospital capacity the death rate will increase rapidly and substantially. No government will fail to act when there are literally bodies piling up on the sidewalks outside of hospitals, so it is much saner to act to divert that scenario.