Without trying to sound crass, food banks _are_ the reason we don't see people dying of starvation in first world countries. If people need food, a food bank will give it to them no questions asked.

The fact food banks exist suggest over all food scarcity is solved in that specific culture. - if it wasn't there wouldn't be any spare food for a food bank

Food is allocated using a variety of mechanisms in peaceful first world countries, primarily money but also via government assistance, kinship, friendship, community, etc.

At any given time many people have problems with one or more of those systems. Money is easy to run out of because it's used for everything, the government can be slow and difficult, relationships can fray, people can be isolated, etc. Food banks exist as a backstop for when the regular means of allocating are not working.

The problem isn't "scarcity" per se, it's more of an allocation thing. Who has a claim on enough food to stay alive? Everyone! But what foods can they claim? How much? What specific channel / institution (with associated allocation rules) will distribute it to them? What are the conditions and controls? etc.

Allocating things can be difficult. An allocation mechanism with no controls will see fraud, waste and abuse. Even when an institution is willing to give things away no questions asked, there are (often invisible until you think about them) conditions like "please don't claim huge quantities and resell what we're giving you, that would be unfair to others".

It's also interesting to think about the fact that you can't fix food scarcity in general by simply giving hungry people money, because money is too fungible.

There's plenty of food, just not the political will to make sure everyone can afford to buy it.

As part of the solution to the hard problem of food: distribution.