I'd go further: many people died because the healthcare industry has embraced efficiency (likely not the precisely right word) at the expense of robustness.
The healthcare industry used exactly that argument to bottleneck the economy and create a lot of inefficiencies so healthcare can't be provided to everyone. Lots of lives would be saved if it got a lot easier for immigrant doctors to practice, but that would be too efficient and not "robust" enough so they can't do it.
I agree that immigrant doctors should have an easier time practicing (and that we should be producing more doctors regardless of their origin). I think that the overall lack of qualified medical workers did lead to unnecessary deaths during the worst of the pandemic.
I think a robustness/efficiency dichotomy isn't the right way to look at this. One doesn't preclude the other. A medical system that is both efficient and robust is certainly possible. This discussion deserves its own thread.