(2) raising prices will always reduce demand, outside of the very specific circumstances where demand is inelastic. Supply and demand is an inescapable law of economics, and subverting it will always result in failures in the supply chain. The scenario you described will also not increase hoarding, it will most certainly decrease it (whether arbitrage trading crops up is a different issue, but one that is completely unrelated to hoarding).
(3) I used the term rationing authority because it was a neutral descriptor. Anybody who acts as an authority on allocation rations is going to be creating the same inefficiencies (though you’d expect the parts of the supply chain closest to the consumers to be the least inefficient)
Most of what you’ve said has demonstrated serious misunderstandings of how the basic principles like supply and demand and opportunity cost works. Your argument that raising prices increases demand should really just be dismissed off the bat.
(2) As I often see when people make the case you're making, you are making unwarranted assumptions about the rationality of buyers. If people are fleeing a hurricane and the gas station raises the price sharply because of the demand, what can happen (and we've seen it happen, in fact) is that it encourages hoarding: it is now a precious commodity and those who can afford to buy it do so, denying it to others.
(3) As I also often see when people make the case you're making, you're also inserting a Big Bad Government Guy into the scenario, your "rationing authority," which people making my case aren't necessarily suggesting at all: we're suggesting that it is rational for suppliers to choose to ration goods in order to be able to meet the demand of a greater number of customers, rather than to meet only the demand of shoppers who can buy as much of [thing in short supply] as possible. Again this is what we actually see in practice, at this very moment: stores in my local area limiting the number of certain items you're able to buy at one time are not doing so because they have been ordered by the California Politburo to do so, they are doing so because on balance they can serve a greater number of customers, rather than turning away literally thousands of desperate people who couldn't "allocate their resources" as well as the guy with five Ultra Transparent Titanium Master Cards.