you are delusional. first of all private boarding schools won't cut it, especially not under democracy. you need an autocratic government to enforce a program akin to ender's game. making such a program immune to corruption is virtually impossible. the kind of utopia you described can only be achieved through brute force and violence, which will surely be followed by corruption.
secondly, how do you reach the utopia you described under one world government? you could have ideologically brainwashed leaders sprung up in a few autocratic countries but how do they come to influence the free world to give that freedom away to people who presumably know better? war? good luck, especially against nuclear super powers. if it's not through war, how do you convince countries that are hostile towards one another or are culturally / religiously incompatible to join into a single block?
then there is the issue of equality gaps. look at europe for example: in the entirely of the migrant crisis only a few million people have arrived. europe has a population of like 700+ million people. in comparison there are like 20+ million illegals in the states which have about half the population of europe. this relatively insignificant amount of migrants triggered the rise of right wing parties across all europe and increased the instability within the block resulting in brexit, alienation of hungary and poland. imagine what would have happened if you decided there should be no borders between africa and europe.
what you described in your essay suits perfectly to the proverb: the road to hell is paved with good intentions. you've described a dystopia.
fixing the equality gaps would require wealthier countries to sacrifice their development or maintenance in order to bring poorer countries up to par, because guess what, resources are finite. do you think any sensible person in a wealthy country would like his standards of living to drop because children are starving is africa? they sure like an insignificant % of the gdp to be spent on foreign aid to feel virtuous about themselves, but that's about it. aside from wealth, how will you cope with the ensuing industrialization? global warming?
finally, how is that great system of producing and providing for everyone going to work? who is the entity behind those actions you describe, the one growing the food, building homes, treating the sick, educating future generations etc? what if you get a shortage of farmers? will this utopian government force individuals into career choices that are necessary for the state or perhaps do what the soviets did and let the less "desirable" regions starve? what if you have too many farmers and you overproduce food? will you burn it away or disallow people to choose a career of their liking because of the excess? same questions apply to any other profession and concern supply demand, but what about payment? after all there is no money nor trade. what is the return for one's work and how will this society decide who is more or less deserving if at all? will everyone get provided for in the same manner regardless of the kind of work they do and how well they do it? if so, what stops people from being "aspiring" artists and leech off society?