Surprisingly few interventions are so good that you don't need fancy statistics to justify them. Really good treatments (e.g. antibiotics) are so effective as to be obvious to all.
To me the real story is that the CDC, which is supposed to be the public health authority in the US, decided not to use said "fancy statistics" and instead chose to only include data that supported their policies. It's the CDC, they should have access to tons of data. Why such small sample sizes?
You mean like the HCQ cures covid research and studeis in March 2020 that "showed" a 100% cure rate that was pushed hard by Elon Musk and an entire political wing? And so many people still believe it, even on HN, it's crazy.