If the cost is too high for a family to buy water, is it more economically rational to then financially donate to one’s own relief effort?
For sure. If you manipulate the price (rather than let the market determine it), you interfere with the market, and hence you will favour and penalize other parties than the one you focus on, as well as changing the signals going to both prospective buyers and sellers. An obvious unintended consequence is hoarding and black markets. You could add rationing — and sometimes that will be needed, for example if the available supplies for an extended period are limited, and it is essential that everybody gets access to essential goods. But rationing also comes with downsides: you cannot always simplify needs down to the same number of X to everyone. Some people may have a specific need for, say, more water than average. And it’s worse still if there is not enough to go around and divided up, say generators or plywood.
The question you never address is: is it moral for a society to expect someone to buy their way out of disaster?
I think that is the wrong question. For me the question is, is it wrong to prevent the market from allowing people to buy their way out of disaster? The best way to discourage frivolous purchases and wasteful usage of something is to raise the price. The best way to encourage sellers to increase supply is to raise the price. The construction worker would not have bothered driving to Charlotte had he not been able to earn more there than at home.