Why would we want to? We already have economic trade with them. What would giving up our sovereignty give us?
Further integration could be good. Imagine if we had a counter to the Euro. Unifying the American, Canadian, and British economies alone would - if memory serves correctly - give the Federation an economy stronger than that of the EU. Even moreso if the "Commonwealth Dollar" or whatever it would be called was in place between them. Picture the economic bonuses of free trade, free movement of labor and capital, etc.
Besides I refuse to live in a country where the occurrence of elections is based on when the queen sees her shadow(or whatever nonsense your parliaments base them off of)
Oh I already took into account how few Americans would accept the Queen. Therefore, two cases:
A. In the case of America joining the Commonwealth, we could be a Commonwealth Republic.
B. In the case of Federation, the Queen would only have status in the states that want her to have it. This means Brits and whatnot can keep their cultural traditions, and we can do the same.
Similar to how I think a federal EU would deal with the monarchies present in Europe.
Unless it chooses to execute them all Commie-style, of course.
On a serious note, this would benefit almost no-one. Economically it would be bad for the US and most of the other nations - Australia may well be the ONLY economic beneficiary of this, due to our economy's focus on natural resources and agriculture - and there'd be massive political repercussions as well. Not to mention the fact that this would actually be illegal in many of the nations involved, specifically the US. It's a horrible unrealistic, unworkable plan.
We could of course, exclude the less-developed nations to make it a smoother ride... once more, though, those excluded would have associated status and preferred status in terms of aid. Only when fully developed could they be integrated into the Federation.
Illegal yes, but that's why we'd have to go through a Lisbon-esque process to give the necessary powers to the C-Feds.
On a personal note, I have no interest in having crazy Americans or Poms telling me what to do any more than already occurs. Although, considering the quality of Australia's current government, maybe if we were part of a federation of sorts the politicians would pay less attention to us, screwing us up less than they currently are.
We don't need to get into nationalities. I don't think ANYBODY wants even their OWN government to tell them what to do(or at least I don't, being a libertarian type).
Hence why the Federation would be very limited in scope and would try to distribute powers evenly amongst the nations involved. The internal differences inside each country would also mitigate things a bit. If we talk the white Commonwealth exclusively, the USA would be countered by 5 other votes in an Upper House, and it's majority vote in the lower house would be split by the Dems and Repubs.
The USA would possess the greatest power in the popularly-elected arena, but the members of this chamber would dilute their own power. Similar to how Congress is in theory the strongest branch of the US, but checks itself with all it's internal divisions, structural and partisan.
As I've said before, if any country runs the risk of having others' will forced upon it, it'd be the United States.
Why would we possible want a place like that to be in the same country as us?
Point taken. Hence why I've developed an "associated status" category for countries like India and the less developed members. These countries would get preferred status for development aid, and until they are fully developed, cannot expect integration into any Federation.