One of the concerns that some (not many) restrictionists occasionally express regarding open borders is that by weakening national boundaries, open borders put us on a slippery slope toward world government. See here and here for instance. While this concern seems mistaken to me, I think it highlights a few important things.
There are two ways of getting rid of vast disparities in the price of a good across different parts of a region. One is to fix a single, uniform price across the entire region and enforce this through regulatory fiat. If, indeed, this is possible. The other is to reduce, as far as possible, the barriers that prevent the good from being transported between the different parts of the region, and then rely on the market’s law of one price to cause the prices to converge. While the law of one price doesn’t work perfectly, it does lead to some convergence in prices and reduction of the vast disparities. Its main advantage over regulatory price-fixing is that it’s better at yielding a correct, efficiency-enhancing choice of price point, and avoid the problems of surplus or shortfalls inherent in regulatory price-fixing.
You can probably see where I am going with this. There are vast disparities in the price of otherwise identical labor across the world (see place premium). These price differences are due to the differing legal and regulatory frameworks, infrastructures, and cultures across the world. One way of trying to fix the problem is to try to fix the issues with different legal and regulatory systems one by one. The most elegant (for some) way of achieving this is world government: have a single government on top that enforces a legal and regulatory framework and promises a certain infrastructure across the world. Another way of trying to fix the problem is to massively reduce the restrictions and barriers placed on migration. While neither will lead to complete elimination of the place premium, the latter approach, when tried, has led to labor market convergence.
The main advantage of freedom of motion rather than the imposition of a uniform standard is that laws and regulatory frameworks cannot be determined by fiat. Like prices, laws need to be discovered through an exploratory process where some things are tried, then altered based on feedback, or borrowed from elsewhere, then adapted. A single world government would mean a single point of failure. The effect of bad laws would be hard to see because there is no control group to check against.
So now, getting to the question of whether open borders will lead to world government. This is very similar to the question of whether unfettered free markets lead to monopolies. I think the answer to the second question is, generally speaking, no, and by analogy, the answer to the first question should also be no. It’s obviously possible to construct arguments that there are various efficiencies of scale with government that make it a “natural monopoly” but it isn’t clear that these arguments carry more weight than the arguments that cut in the other direction — namely that governments that deal with smaller populations tend to be more responsive to the needs of the populations and the populations themselves tend to participate in government to a greater degree and with higher rationality (because they have a higher probability of influencing the outcome).
That being said, there may be a role for various international agencies and advisory bodies to help govern and coordinate international labor flows. In his article Open Borders with Migration Taxes are the Best Policy (which he blogs about here), Nathan Smith proposes the creation of a World Migration Organization which would play a role analogous to the World Trade Organization.