What if food bank clients could buy extra food via food banks?

Two pieces of common knowledge:

1. Donating money to food banks is more efficient than donating food, because they can use the money to buy food bulk and/or wholesale.
2. Sometimes food banks run low on food.

Suppose you're going to a food bank because you can't afford enough food to get your family through the month. And suppose this happens to be a time when the food bank is running low on food, and they don't have enough to give you (or they don't have enough of what you need to give you). And suppose you have a little bit of money, just not enough to get through the month. What if you could give the food bank what money you have, and they could buy food for you at much better prices?

Of course, it's debatable whether this is ethical. Letting people buy better treatment from food banks doesn't seem entirely consistent with the spirit of food banks. But, on the other hand, saying "If they have extra money they should be donating it when the food bank is short on food!" seems very nearly victim-blamey. Perhaps the solution would be somewhere in the middle - X% of clients' donations go to general food bank coffers, Y% can be used for the donor-client themselves. But that seems a bit paternalistic, like parents who dictate how much money their kids need to give to charity.

I don't have answers, but I think it would be interesting to study and do projections (if they haven't already), and perhaps do a temporary pilot project to see what happens.