Agreed. I think the military model is an excellent example of how to work both sides of the equation. Private industry is not, independently, sitting in a room dreaming up new guns and tanks and ships and planes. The military shares information about what works in the field, what does not work, what they need, etc.
The Declaration of Independence lists our unalienable rights as life, liberty, and the pursuit of happiness. The Preamble to the Constitution states that we are creating the Constitution to, among other things, insure domestic tranquility, provide for the common defense, and promote the general welfare. As someone pointed out earlier, we can even envision the defense against pandemics as a national security issue. So there is plenty of room to establish a federal interest and a federal role in defending the country against pandemics. Something that is more powerful than the cynical arguments for federalism ("let the states do all of this") or capitalism ("let private industry do all of this").
You are correct, corporations are, literally, supposed to operate as sharks, devouring everything in their paths in the pursuit of profit. It would be very difficult for private industry to have employees all over the globe simply to do the research and data collection on novel viruses and novel strains of the flu and other diseases. Governmental and quasi-governmental agencies can do that.
And once there is research and data, the government can share that information with American private industry, which has the muscle to produce and distribute innoculations and vaccines. In fact, that's pretty much the system we have now (with several substantial imperfections). When WHO distributed the COVID-19 genome-typing and the blueprint for a testing kit in late January 2020, it was never supposed to be left to the CDC to then "manufacture" those testing kits, it was always going to be private industry that did that. We just have a ****-poor communication and sharing system (particularly since the pandemic response unit within the NSA has been dismantled), not to mention a president who would then choose not to immediately use the Defense Production Act to authorize the mass-manufacture and mass-distribution of testing kits across the country. Because he doesn't like testing. Because then the numbers would be higher.