I'd argue that lifting price controls is rationing. And it frees the merchant from having to try to keep track of who bought how much and when.

Long term, rationing might be the way to go. In the short term (like, the S just HTF), basic economics (supply and demand) have a better shot at making goods and services available fairly.

I hate to say it, but the poor are going to get dumped on either way. At least with economic rationing (allowing the price to respond to demand), they have a better chance of getting a bag of ice or a gallon of gas if they really need it.