[hibikir]

When the supply of something is lower than the number of people that are price sensitive and desperate, capping prices will still leave desperate people without what they want. Many mechanisms that appear to be more fair, like free lotteries, end up distorting things in other ways: If it's a free lottery, you bet people will sign up without being desperate.

One might have an aesthetically favorite version of deciding who is going to go without, but there's always going to be a problem with just that. What really helps is increasing the supply of what people want. And for that, it's hard to beat increasing rewards to the suppliers.