> If the world is governed by rules, why does the United States maintain a considerable number of military bases around the world, far exceeding the total number of military bases of all other countries combined?

It's the other way around. Rules are tools of peace. No peace, no rules. But if you want peace then you have to be ready to wage war. It's called deterrence and the EU is learning this just now, again. That's also one reason why the USA has been called the world police... because it was true.*

If nobody enforces the rules any more, things break down and we close in on violence. It is plain to see on the global scale, e.g. Russia's war against Ukraine, and also the domestic scale, e.g. ICE's violence against their own citizens in the USA.

> Why is the American military budget so much higher than the combined military budgets of all other countries?

The US military budget is about three times that of the EU or China's, or about a third of all military spending on the globe. Obviously, this is much higher than any single entity, but not all other countries combined.

* Frankly, being the world police has had a lot of benefits for the USA. Why they are abdicating this position to run a protection racket instead is for wiser people than me to answer.