Here is an example of what they are trying to solve by flattening the curve. https://www.livescience.com/coronavirus-flatten-the-curve.html As you can see from this model, while there aren't as many early exposures there are more later exposures and stretched out over time. Part of the mitigating is based on humans actually being exposed to the disease and letting the body naturally do its thing. Most all Americans will be exposed in some manner but might not necessarily have noticeable symptoms."Social distancing and shelter in place are designed to drag it out longer." check out the definition of mitigate. it says nothing about dragging it out = the action of reducing the severity , seriousness, or painfulness of something. while I do agree that this mitigating practice does take a little time; thus your comment. But what they are doing (mitigating= social distancing) is NOT designing to drag this out.
the same amount of people are going to be exposed This comment is unprovable