Given that there's an accute shortage of hospitals serving rural areas, regulation of that nature better be accompanied by federal funding for that work.

I wouldn't be surprised to see some serious DHS money redirected to hospitals, after this is all over. They could certainly put it to better use than police departments.

Alternatively, you could assign maintaining the mask inventory to admin staff. I know they often don't have advanced degrees, but I can't imagine they'd do a worse job of it. Actually, they'd probably take the job a lot more seriously than the "experts" who are in charge currently.

Assigning such tasks to a central body seems like an extremely fragile design, and as evidence for this assertion, I offer the current state of reality. I find it a rather convincing argument, but then I'm probably quite biased.