I think you're misunderstanding me. It's my claim that any sufficiently profitable colony sufficiently far away from its mother country will inevitably cease to be a part of said mother country. The how is irrelevant.
Your claim is wrong.
That's how the history is written, yes. And how the history is written...is irrelevant. Where are all these profitable, distant colonies with voices in parliament today? Australia? Canada? Technically not sovereign, but they operate as separate nations. No country in the world fits the description of the U.S. you claim would have otherwise been inevitable, and you don't give this a second thought. The oldest truism is the ephemeral nature of Empire. You let your piecemeal study of history delude you.