Of course the "other" cause may be to make a backup of the Earth civilization and humankind for a case of collapse on Earth, due to global warming, an asteroid impact that hasn't been averted, etc. But this is only possible with true material independence, such that can withstand any blockage or embargo from the Earth's side, else it won't stand the collapse on Earth. The colony may declare allegiance to a particular Earth's government, and inherit the civil norms from the culture(s) which built it, but cannot and must not be ruled from Earth.

Independence != animosity and bitter confrontation. It's more like Canada is independent from the UK, despite some formal allegiance, and the UK is not going to send troops if the Canadian parliament votes in a way that bothers the English monarch.

This is a colossal task, likely not achievable even in this century with the technology we currently have. Stuff like high-temperature atomic engines and other near-sci-fi stuff could alter the equation somehow.