I agree that relatively small improvements in public health could potentially be highly beneficial. Research on this might be totally tractable.
What I am concerned might be intractable is deploying results. Public health (and all health-relevant products) is a massive industry, with a lot of strong interests pushing in different directions. It seems entirely possible that all the answers are already out there, just drowned out by food, exercise, sexual health, self-help, and other industries.
There’s so much noise out there, it seems unlikely that a few EAs will be able to get a word in edgewise.
I agree on the challenges of deploying results. I think the primary value in public health research is empowering individuals to make good decisions for themselves. For example, sites like WedMD and Healthline add a lot of value for individuals trying to improve their families’ health. I don’t think the answer is already out there on obesity and many other chronic diseases. If it is, I would appreciate someone directing me to it. :)