If there was one worldwide government, how would you avoid regionalism?

If the people of the world voted for representatives in the worldwide government, those representatives would try to use their political power to benefit the people who voted for them. That's how representative democracy works.

If you had proportional representation, then representatives from China, India, and Africa (even if those countries/continents no longer existed as distinct political units) would have a big chunk of the say-so in government, and could introduce laws and policies that would benefit the people who voted for them, at the potential expense of other areas.

You could do away with proportional representation and just give each continent the same number of representatives, but then you have to deal with the fact that the voters from Australia (0.3 percent of the world's population) controls one-sixth of the political power. Even if you split things up differently, you still end up with regions, each of which will vote for representatives who will do things to benefit them.

A functional world government, in theory, could do away with war (though in reality you would probably be dealing with dozens of internal rebellions of varying sizes instead, trading foreign armies for armed dissidents). But getting rid of regionalism seems like a tough nut, unless you put the world in charge of a dictator (and then the regions would still try to curry the dictator's favour).