I'm inclined to believe that also has a lot to with how populated those colonies were and how much of a strong system already existed.
USA and Australia are mostly European immigrants. Those were vast, sparsely populated lands with local population living in nomadic lifestyle with little or no centralisation. Europeans arrive, local population is assimilated, exterminated or ignored, and it was easy for Europeans to set up a system, any system, and make it work.
That's a stark contrast to India for example, or even Dutch colonies in south-eastern Asia.
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