Regulatory capture is a universal problem as long as a government is involved in an economy, and it has to be if for no other reason than to collect taxes.
Going back to farming, the Federal government assumed near total control over a great of it in the New Deal, down to how much you could charge for selling a kosher chicken (A.L.A. Schechter Poultry Corp. v. United States "the surname Schechter means "slaughter" in Yiddish, and specifically refers to a ritual slaughterer") and the two have been inextricably linked since then.
And until about now things have been a lot better, for before WWII at the same time food production was limited by diktat and there were newsreels of it being destroyed, the USDA also believed about a quarter of the nation was malnourished which was confirmed in the WWII draft. Which I've read was major factor in establishing the school lunch program.
They could solve the baby formula immediately by just allowing import of European baby formula. Sure, it’s not been vetted by FDA, but unless you believe French or German babies are malnourished en masse, this is scarcely a good reason to prevent import in time of shortage.
And if babies die of malnutrition that’s not their fault and won’t affect their performance review.
As for stores not providing baby formula recipes, I'd imagine they're worried about liability, and there are of course many other sources for them. Really, due to the Federal government's WIC program which is half the market, its import restrictions, and messed up FDA regulation it should be on them.
I say messed up because the FDA demonstrably wasn't serious about dealing with the Abbott Labs plant problem or getting it fixed quickly based on the timeline starting with the whistle blower, while they make it very hard to get into the business. Or the USDA's problem due to their policy of forcing states to grant a WIC monopoly to one formula manufacturer resulted in three companies having almost all the total US market with Abbott having the largest share, at the same time US prices being double those of Europe. Which isn't as strict about food safety but still seems to do OK.
A serious country would have done something to mitigate the shortage after they closed down Abbot's huge factory before there were bare shelves for months and it became a political problem in an election year.