This doesn't seem like a very good alternative. Even with adequate hospital care, the true fatality rate seems to be in the neighborhood of 0.5% to 1%, which would be quite harsh if allowed to spread throughout the population.
I am hoping that improvements in treatment can make the difference. A vaccine may not be available for quite some time, but drugs that reduce the fatality rate might be ready sooner.
Of course the actual course of action must include some mix of all-of-the-above: containment, new hospitals, new treatments.
EDIT: as voidmain notes, we might also hope to quickly reduce the number of infections to the point where we can contain them with testing and contact tracing, rather than blanket shutdowns.