I don't think the price is the problem. I couldn't get toilet paper for a week, not because some enterprising con-man had purchased it all and was selling it for 10x as much outside my door, but because ordinary folk at the tail of the distribution bought it all at its normal (low) price and we temporarily ran out of supply.
What we needed was immediate rationing policies, the price was never the problem. Stores eventually ended up self-initiating individual buying limits but this was well after all the initial supply dried up.
In fact, if all prices were immediately responsive to local supply/demand, this likely would have effectively resulted in a rationing policy. If the unit price of toilet paper at my local CVS was in part a function of the remaining supply at the local store, as one person attempted to buy all of it, the unit price would soar, effectively preventing them from doing so unless they're a millionaire and prepared to spend thousands of dollars on toilet paper.
Indeed, one can easily make an argument for stronger market forces to solve this problem. That existing markets for common goods are too poorly responsive to supply and demand and that the local supply/demand signals are ignored and only national signals are accounted for.
But also, simple rationing would have worked too.