You are correct that social distancing and flattening the curve protects the health care system from overloading. That doesn't mean that it is the only purpose, or effect. If we took a poll among health care policymakers about the benefits of flattening the curve, I'd be happy to bet any amount you'd like to wager that "buying time to develop effective treatments or a vaccine" would be on their list.
This is the key takeaway from “flattening the curve”. It cannot and will not decrease the total number of people who are ultimately exposed at this stage of the pandemic.
This is just mathematically untrue. There is clearly a point where the curve is so flattened that the number of deaths under it is less than a baseline "no action" scenario. If we could somehow get everyone in the US to truly isolate for three weeks, the virus would die out entirely. So clearly there is a spectrum of actions and their corresponding outcomes. The number of infected (and dead) is not a fixed number with only the duration of the outbreak changing.
If your premise were simply that the current measures are unsustainable, I couldn't agree more. Fortunately, those measures have bought us the time to take more focused, informed action based on the latest data. In a crisis this fast-moving, every day is time to update the policy.