My question is, would this be possible in today's or near-future
society and is it as good an idea as I hope it would be?
Since your question implies whether we should consider a practical transition to something of an emergent global civilization with a mostly singular identity, then we should probably talk about the time horizon of its achievement.
Yes, I would also agree that this would be the ideal ultimate form of human civilization, so long as this entails that the end result is some kind of merging of the purportedly 30-something major global civilizations in existence today, and not some kind of purposely or even accidentally forced sterilization of the vast wealth of culture our planet currently possesses. Full globalization might take place on as long a horizon as some 500 to 1000 years yet, but don't quote me on that. But first, we would have to consider the thermodynamic costs of change in the social and economic institutions that would be required to bring about such a unified global civilization.
Rapid globalization comes with frictions. If labor markets are displaced too rapidly by technologies of a nature that generate scale-free increasing returns for an increasingly small proportion of the economy, then the losers of that exchange, if not strategically compensated by some form of social redistribution (viz an overall Pareto improvement), may feel victimized and hence coalesce behind nationalistic political parties that promise to restore their former living standards through trade protectionism.
We are seeing this very process unfold today all across Europe and perhaps the United States. We also saw this near the end of the second Industrial Revolution at the beginning of the 20th century just prior to World War I. I strongly believe there is a connection here that should not be dismissed as simply some kind of irrationality that will eventually correct itself under the guise of the Invisible Hand or other market forces.
In economics, there is often a myopic focus on the long run because that's all economic models can for the most part can predict, but in history and politics what happens in the middle is just as important as what will likely happen in the end. In summary, we should not ignore Luddites, because it is not fear of technology per se, but fear of social exclusion due to technological change, that generates large scale waves of sociopolitical unrest.
What we certainly do not want happening is a repetition of the kind of experiment entailed in the formation of one authoritarian German state from the 1930's. The problems there are especially salient. In effect, the vision was the creation of a global space for a certain kind of invented class of privileged individuals at the expense of anybody who was perceived to be even remotely different. That this was patently wrong goes without saying.
I would conclude by saying that even the relatively tame post 1970's neoliberal tradition of expansionist free trade in the form of Reagonomics and Margaret Thatcher's United Kingdom was also preemptively hasty, the affects of which are only now being felt. Barring significant changes to inherited Millenia-old psychological predispositions for the formation of networks of power relationships and groups, I don't think we'll see a truly singular global civilization in our lifetimes.
One thing to really keep in mind is that a civilization in which all income is rewarded meritocratically, i.e. without political, cultural or geographic barriers, is that when technology markets change in terms of how they favor a certain kind of new labor or capital input then so do the customary lifestyles of large groups of people (even very small initial differences in conditions between labor pools at that scale could lead to rapid propagation of income inequality between as-yet new groups not related to any particular nationality), and that doesn't come without consequences.
Rapid changes in wealth can destroy the social fabric of working communities, whether that community happens to be "taxi drivers globally" or "lower-middle class manufacturing workers in the Midwestern U.S." The rate at which these dislocations occur can probably be optimized by understanding that all changes to social structures come with a real energy cost, because human relationships are expensive things to build and maintain, and that these costs can be mitigated by modulating the time horizon of a society's introduction to freer trade, i.e. by defining and monitoring industries where the medium-run affects of globalization are the most prone to generating economic frictions.
I strongly recommend you read some of the works of Stuart J. Kauffman. In particular, "At Home in the Universe" for scientific context and his latest "Humanity in a Creative World", a political and spiritual work. He's a medical doctor turned microbiologist turned complex systems and networks theorist who draws on a multitude of interesting parallels between systems as diverse as mitochondria and cities. Kauffman talks about how "patches" and decentralization lead to the most effective political "computations". While I do not have the immediate wherewithal to effectively summarize his works here, I think that's probably the closest you'll get to finding a technically satisfying answer to your question at a level that is easily digestible.