The free market is not designed at all to do anything, let alone acts with a bolted-on moral load.
What the free market allows is that economic actors like the hospital are free to purchase their supplies from anyone at all from anywhere, and allows anyone who has any interest in producing said supplies to present their offering. That's it.
I live in a country where, when the demand for N95 masks started, had a few unrelated corporations quickly enter the market with their own product. I'm talking about companies ranging from office supplies to coffee makers. Hell, even beer producers quickly entered the hand sanitizer market. Consequently prices dropped drastically and not only is there no shortage of protective equipment but it's also affordable.
That's what happens in a free market.
How come you're talking about this sort of stuff not happening in your country, and still you talk about a free market?