re: I'm not sure our world is big enough
Your idea would only work if it were a world confederacy with all military power in the hands of the confederate governmental unit.
Nothing new there, you're just describing the Federal system already in place in the US. In theory it was supposed to allow maximum autonomy for the states, within a protective confederation to provide for the common defense. Scaling up the system to a global level carries no more risk of tyranny than at the scale of a single nation...which is to say, not zero, but mitigated by the decentralization of power. It's the best system we've invented so far, and I have a little trouble understanding why Conservatives don't have faith that it would work on a planetary scale. Perhaps it's just the emotion of nationalism triumphing over common sense--better to be a big fish in a small pond.
Sounds like you get my point pretty well, actually. Let people seek their own happiness as they define it, to the extent that they don't infringe on the rights of others to seek their happiness. People instinctively feel more comfortable around people with whom they have a lot in common, and the practical advantage is that in a congenial culture a person will perceive fewer apparent obstacles to happiness (disagreement has a way of showing up as opposition; fewer apparent disagreements is perceived as less friction in life). Trying to impose a uniform national culture is suboptimum except for the tiny slice of people who happen to be a perfect fit with that culture.