I'm curious. Do any of the same people who think we don't need a world government think that the United States (or, depending on your own location, your own 'federated' government) doesn't need *its* government and that all of the states should be individual countries?
It's different for countries because there's something outside to unite against. (One view of Canadian Confederation is that the different provinces united to stop from being annexed into the US.)
In some countries there is such a thing as devolution. People feel more confident with local administration. They know that with that, their needs won't be ignored as readily, even though it costs them more in overheads.
One of the fears of broader governments is that revenue which your locality generates, gets diverted away from your locality towards the 'wealthier' and 'popular' areas.
Such happens all the time: The roads in your town get maintained, but the ones in the town centre get the most attention because they're on public view, and the towns "image" is judged on those. If you live on the fringes of the town, your road might be in poor condition, and it rarely get maintained because it's out of public view, so it's a low priority and it gets routinely ignored.
Or, the other way around, it gets sent to poorer areas through equalization.