But a lion and tiger are biologically different. All humans are the same, regardless of skin colour. And saying that the world would be one country does not mean the end of culture. London is markedly different to New York, or even Glasgow. This would not change. As it is, globalisation means that the world is becoming homogenised, and we are seeing McDonald's in Kabul and Baghdad, Moscow and Paris. Places are starting to look the same anyway; removing arbitrary boundaries isn't going to speed this process up, if anything it will slow it down because there won't be 'new markets' for companies to move to in the same sense as now.
And why wouldn't it work? It used to be that way before we decided that might was right and we should have wars to protect territories. I mean, what if an alien race attacked us tomorrow? We would unite, and we would feel like one planet. One planet of humans, against the rest of the universe ooh rah. There is no reason we shouldn't aspire to this now.