You might as well argue that it's impossible to distribute beer to a country of 320M people, yet inhabitants of large countries don't go thirsty.

Whether we talk about a union of 320M as the US or a union of 510M as the EU, or whether we talk about a state like Michigan with 9M inhabitants or a nation like Sweden with 10M hardly matters. There are roads, electrical grids and similar infrastructure everywhere in the modern world.

It's not the distribution that's the problem. It's political will.