You're right, that's a relatively minor concern. How about the concern that the existence of a single government doesn't stop people shooting at each other, as

You're right, that's a relatively minor concern. How about the concern that the existence of a single government doesn't stop people shooting at each other, as indicated by, oh, say, the Syrian Civil War? Even in the optimal case where you somehow did achieve a one-world government that was democratic and benign (rather than resembling the average government) you would inevitably have groups of people thinking that this is a non-ideal government whose authority should be challenged. In the end you'd just wind up replacing all ordinary wars with civil wars. And the civil wars, instead of being confined to one country at a time, would rage simultaneously in all countries, always.