"What sort of organizing principle would the world have then?"
I don't know if this is what is likely to happen, but I've been pondering this: The Westphalian order for the world, which we currently live under, involves drawing borders for countries, and then basically insisting that the governments within those borders must have some sort of unity, regardless of what those borders are, do, or come from.
Do you have a group of people that are geographically localized but have borders going right through the middle of them, like the Kurds? Then they are not a country, not countrymen, and regardless of their affiliations they are subject to their country's policies for dealing with each other. The split of East and West Germany was an extreme case of this, where a national border was drawn, and you had families cut in half.
Do you have bunches of people that basically loathe each other with the fire of a thousand suns, but there's a border drawn around them on the world map? Then they live together, until the most pathological cases like Yugoslavia finally just blow apart.
And where did these borders come from? Did some bureaucrats in Europe in the 1700s or 1800s draw some conveniently straight lines in Africa? You're a country now in the 21st century, regardless of how anyone local feels about that. Pretty much anywhere in the world you see a straight line border you see something very artificial that took no account of conditions on the ground.
In the 1990s, the cyber utopians thought that technology would lead to more decentralization. With improved technology, you don't need industrial-era practices to deal with cities and counties and states and countries. You can have very sophisticated government and government services now at much smaller polities; even the small local cities take online payments now, for instance, and have online billing.
Perhaps the future looks like the Westphalian system cracking up, and polities being more willing to secede, easily join together in arrangements of convenience as needed, and easily break apart again as their interests diverge. There are certainly a lot of practical issues involved in that transition, but as diversity increases all around the world, there's increasingly a lot of practical issues involved in forcibly jamming people together because of borders drawn 200+ years ago. It wouldn't solve war; that's not on the table. But it might just prevent World War III.