In what ways did the American colonies need Britain, and in what ways did they not?

It's an
interesting question, though I should add that the American colonists viewed themselves as
British for most of their history. The colonies were an extension of Britain. With this in mind,
viewing this relationship solely in terms of dependency underestimates the strength of those
ties.

Beyond this, the colonies did rely on Britain in certain respects. In
terms of economics, Britain was their primary trading partner, and after independence, a
critical task for the new country was creating an economic apparatus which could replace the
loss of those ties to Britain. In addition, so long as they were under British rule, they could
count on at least some measure of British protection, particularly when it came to other
European nations and their American colonies.

On the other hand, we should
note the sheer distance between Britain and its colonies, which left the colonies with a long
tradition of self-governance. Even when we note that Britain did...