[Not historian] it's due to the way of colonization by each European power. For example, in South America the major colonizers were the Portuguese and Spanish. The way they colonized was mainly for economic advantage, single males would come to the New World and try to attain money. They did not really bring women with them so they tended to marry Indigenous people so there were lots of Mestizos (Latin American and European) people, combining the cultures of the Europeans and South Americans.

While in North America, Great Britain tended to dominate. Their colonization policy was basically push the Indigenous people west, because the English brought families so they didn't need much intermarriage so their cultures didn't really combine as much as in South America. Also, the British were very influential in the colony's government, but the Spanish and Portuguese let their colonies have more autonomy. This allowed the culture the colonists had adopted to influence government. So after the Revolutionary War, the United States basically adopted the same principle, and continued to push west while forcing the Indigenous people into small areas.

Again, I'm not a historian so please don't take this as the right answer.

In Australias case the land was essentially seen as empty, or emptyish. Australian Aboriginal tribes were small and not clearly organised by Western standards(no 'Sioux' nations here (and yes I know the greater organisations of NA tribes came a bit later)) thus no treaties were signed and no formal agreement of who owned what and where could be made. Making Australia a free for all. Subsequently Australia was almost entirely made up by British settlers. Ive read figures in the past, cant find them now, that suggest that at the start of WW1 Australia was more 'British' than Britain, in that a greater percentage of its citizens had a British background than in Britain itself, due to heavy immigration to the UK over the previous 50 years. Australias 'White Australia' Policy also prevented non-europeans from going there, this was finally overturned in 1973. Thus Australia was almost 100% 'western' up until 30-40 years or so.

New Zealand ran a similar course, although their interactions with the Maoris were more complex and the percentage of Europeans is a bit lower there.

Essentially these two countries were entirely created by westerners replacing the original inhabitants and any sociopolitical structures they may have had. As others note, this was not true of South/Central America.