> What bothers people here primarily is that hoarders made money while everyone else is suffering.

No, what bothers me is the assumption that "higher desire" means "more willingness [and ability] to pay," and that "more efficient" means "assigned to the people with higher desire." For reasons of life and death (which I, personally, find more important than the principle of a free market), I think a "more efficient" tool should be one that distributes to people with higher need, and need is generally not correlated with ability to pay. It may even be inversely correlated: I as a tech worker can just stay home for weeks, and I haven't needed a drop of hand sanitizer. Someone who drives buses or makes hamburgers can't do that and must be out in the world for their job, and their jobs pay them a lot less than my job does.

So, government rationing would be an "efficient" solution in my definition, yes, but there's a milder option here: use the government's influence to artificially prevent the price of the product from rising. Then there's no incentive for people to buy large quantities with the purpose of reselling it, and it's more likely that everyone will buy the small amount that they need.