It's called United Nations Organization. Although it hasn't been fully implemented. It was planned to have nuclear weapon monopoly and strong joint military forces to stop any aggression. Why didn't that happen? Because it's the US that gained the benefits out of both world wars. And its allies aren't allies but minions. Remember what happened to Charles de Gaulle?

Also note that no one has ever declared a war legally since WW II. Because of the UN and international conventions.

I'd also add that it's not entirely correct to consider countries equal top level actors in the historical process now and in the past. Nowadays so called political nations are technically subjects of international right, of course. But, for instance, in pre-Westphalian world that wasn't the case and these days there is plenty of evidence of transnational actors' influence. For example, Vatican dates back to that era I mentioned. And also who owns most the land in Europe? And how come these von Something German nazis avoided The Nuremberg Trials and ended up as board members in big industrial companies?

So no, the world doesn't need a hegemon in your sense. Taking into account the paralysis of the UN since 1991 it's more likely there will be another take on the ruins that.

Maybe so, maybe not, whatever. None of that changes my point: you'll get a 'hegemon' whether you want one or not, and no, it won't be the UN. It will either be a US-led alliance or one led by China. The world is becoming more polarized, not less, and I don't see how that trend can be reversed.

By the same token, at the national level, it's possible that dictatorship will emerge as the only stable model of governance. People everywhere seem to want it. The only principle that actually matters in politics turns out to be "Screw the other guy," and dictators are the best at that. If so, the US's ability to protest and resist its central government will turn out to be maladaptive, giving the advantage to the China-Russia alliance in the long run.

As for the church, they still own the land but not the hearts and minds. Or the nukes. Religion is irrelevant at the international scope. But of course it's still as useful to the rulers of individual nations as ever, because you can't maintain a cult of personality without exploiting the same mental bug that the church originally stumbled across.

I believe that US has been an essential partner for a very long time. It demands great leadership but it is something sorely lacking over the past couple of decades.