Australia has made a bunch of home-ownership-unfriendly decisions which the US hasn't – e.g. in the US you get a mortgage interest deduction on your primary residence, in Australia you only get it on investment properties (joint filing for married couples, which the US has but Australia doesn't, also helps here); in the US owner-occupier mortgages are normally no-recourse, in Australia they are almost always full recourse; US government policy encourages long-term fixed interest mortgages, the Australian government has no comparable policy
Some of it is also geography – Australia is very centralised, with most people living on the coast. Each state has its population dominated by a single metro area which also serves as the state capital – quite unlike the US where majority of the time the state capital is outside the state's largest metro area.
Australia's comparative lack of rainfall inland is a factor, but political culture, and hence decisions by politicians, also plays a big part – suppose NSW moved its capital to (say) Dubbo or Bathurst? Many government jobs would leave Sydney, followed by many consulting/etc jobs which provide services to the government - right now, central and western NSW has plenty of affordable housing, but a big shortage of jobs providing incomes to pay for that housing. Never going to happen: it would require a degree of originality and thinking outside the box of which Australian politicians are constitutionally incapable.