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.