What you are missing of course, is that there are simply not enough shelters to go around. You also hadn't considered the fact that housing in Australia, is no longer cheap, thus unaffordable with Centre Link payment on the private market.
Besides being unaffordable there is a lot of stigma, deliberately fanned in cases by authorities blaming the homeless for predicament, which in turn means very hard to rent on the private market.
As I noted earlier, many shelters are at best band aid measures, allowing respite and a roof for a limited period of time. It could be a few days to a few months but under funding reg's there is too, often a time frame involved.
This country is crying out for affordable shelter. The situation will only worsen unless the will develops to turn things around.
I wonder why you consider people would make a deliberate decision to be homeless? In a land of next to no security of rented tenure, limited rental government allowance, few state housing options, high immigration, it is little wonder that vulnerable are cast aside.