Why did Britain refuse to immigrate to America?

First, the first British people who came to North America hundreds of years ago were mostly pagans of the Anglican Church, that is, Puritans. They hate British rulers, long for freedom and independence, and don't like being bound. These immigrants later became the majority of the American population, and they didn't like Britain at all.

Second, when the Commonwealth was founded, the United States was already extremely powerful and was already fighting for world hegemony. How can it be willing to join the British-led Commonwealth?