You missed the mathematical reason for the two party system. It is a systemic property and two parties are the most stable state. ..and the people in power know this. Bribing and coercion is more efficient if you can limit the number of people.
If you wanted Australia or USA to have more than 2 viable parties, all you would have to do is change how votes are cast. Instead of the winner takes all system, do something like have voters order the candidates by preference and sum the preference totals. If there are only 2 candidates, it reduces to become identical to the current system. With more than 2, diametrically opposed parties cancel and a voters 2nd or 3rd choice would typically be elected.
Thanks @dsonophorus for this information. I was thinking it would be better not to have any parties. The parties themselves act as control mechanisms even in a environment where there are more than 2 viable parties.
Are you referring to the famous results in the mathematics of social choice theory?
Australia already has a preferential voting system.