"What if we all shelter in place but hospitals end up overwhelmed anyway? That seems like a real possibility and it kind of makes the argument irrelevant."

There aren't just two modes: Hospitals OK and Hospitals Overwhelmed. The idea behind flattening the curve is to reduce the burden on the hospitals to whatever degree is possible. How is it "irrelevant" if a hospital is 200% over capacity versus 500% over capacity? The people who would die in the worst-case scenario but not in the "flattened" scenario would probably think it is extremely relevant.