(This is a follow-up to my previous post, "Democracy - it doesn't work", and assumes you have read that first.)
Suppose many countries did indeed adopt this "go anywhere, settle anywhere, work anywhere" policy. In fact, let's suppose that every country except one does. Often, one selfish person in an altruistic group gets all the benefits and none of the costs (eg the tragedy of the commons), encouraging that person in selfishness, and turning the entire group to do the same. Can the free movement outside a country prevent this failure, or would this system require international treaties forcing all countries to grant freedoms?
Firstly, as we've already seen, tourism benefits from reduced barriers. Tourism brings economic benefits, so there's a fairly direct financial incentive to encouraging it. Secondly, it'll be the more welcoming countries that people want to move to (for whatever definition of "welcoming" each person chooses), so it'll be something worth bragging - we have open borders, come to us! Both phenomena can be seen today - the latter is best seen with ADSL "Fast Churn", which is an advertisable feature for ISPs that basically means you can hop from one provider to another.
Secondly, when freedom is the expected norm, people will tend to subvert or ignore anything that works against it. Look at how many places there are to illegitimately download software, music, movies, etcetera, etcetera, etcetera. The individual citizens are the ones who benefit the most from freedom and the least from restrictions, so the tendency of seven billion people will be to pressure governments into freedom - probably by subverting the rules and just walking out. For a single totalitarian government in a mostly-free world, the country's extents will be based on how much land and how many people they can dominate by force. If critical mass can be achieved, freedom will win. Again, for evidence, just look at the internet, where this already is happening.
So if there's no border controls, what's to stop people from evading taxes whereever they go? Well, that'd ultimately be up to the individual governments, but IMO the easiest solution would be to base everything on a sales tax. Any individual or business with annual turnover in excess of some threshold can send some percentage of revenue to the king. But the higher your tax rate, the more likely for people to leave - or rather, the higher your tax rate compared to your neighbours. That's going to produce a notable feedback loop; countries that abut will experience "border hopping" according to the price difference between them. As long as that difference isn't excessive, the hassle of travel will restrict this to those who live right by the border (as already happens with the CA-US border, for instance), but it could be a huge difference if one country uses a sales tax and the other an income tax. It'd come down to individual governments' decisions based on their neighbours, just like any other company choosing how to price its services. As a bonus, this would strongly encourage a country to have low taxes, as that both makes you look better (compared to the tax rates of your neighbours), and gives you more flexibility (if everyone's taxes are low, the differences between them aren't significant, and the hassle of travel isn't worthwhile).
Centralizing too much power creates corrupt leaders. Decentralization, putting the power into the hands of individuals, will tend to restrict government and ensure that the stupid and/or evil leaders can't do too much damage, and have an incentive to be less evil.
Ultimately, we're all equal before the One primary Power in the world. A political and economic system that reflects this will work where others fail.