Could a conceptual country function?

I've been thinking recently about the idea of a conceptual country. The same sort of thing as John Lennon's 'Nutopia'. Of course, on closer inspection, Lennon's country was really an incredibly clever failed attempt to stop himself being deported. But the idea is still good.

I actually think that the idea of a conceptual nation could be taken much further, and could make a real impact if it was supported enough. So, I've actually got some ideas for how this thing could work. This is a little complicated to put across so bear with me. For the purposes of explaining, I'll use Lennon's name 'Nutopia' for the conceptual country.

BORDERS

Nutopia has no land borders. Anyone can become a citizen of Nutopia regardless of their geographical location.

TAX

The citizens don't pay taxes to the governments of the places they happen to come from anymore, now they pay taxes to the central, elected government of Nutopia. Because Nutopia doesn't exist as a location, very few facilities are needed for the nation itself. Instead, taxes are used wherever they are needed most. The government decides where different sums of tax money should go based on factors such as: How much money does Ethiopia need? How likely is it that the Ethiopian government will get the money on their own? Is there a possibility that money will be mis-used if we give it to Ethiopia? etc. Not only does this mean the money of the world is spread more evenly; This way of doing things also means that as the population of Nupotia grows, it becomes massively influential on world politics.

HEALTHCARE

This has it's own section because I just realised that if I stopped paying taxes to Britain, I would no longer be entitled to the NHS. I have a solution, the government of Nutopia pays for the healthcare of it's people. According to the BBC, the NHS spends about £277 per person, per year on average. That's including checkups and dentistry and operations and medicine and everything else. So Nutopia reserves about £300 of tax money per person for people's healthcare. This money would be available for citizens to pay for healthcare in their own countries.

POLITICS

As I said before, a large Nutopian population allows the nation to have massive influence on world events. It could even be used to stop wars in a way such as this:

1) Country A invades Country B.

2) Nutopia immediately cuts all funding to Country A and funds the defence of Country B.

3) Country A is unable to cope with lack of funding for the war.

4) War ends.

I genuinely believe that if an entirely conceptual country existed in this way, it would help to maintain a more peaceful world in general.

So the question is: Are there any massive, glaringly obvious holes in a plan such as this that I haven't noticed for whatever reason?