This is such an interesting and well-argued take that I want to engage you on it simply for the sake of discourse, but not being that knowledgeable about Australia's specific biosecurity restrictions I'll only make two general points and acknowledge that both may be more complicated than I'm positing:
(Also, for what it's worth: my second point may be moot based on your interpretation of "conservation program" potentially not including the simple breeding of endangered species - but not being privy to the hippo conversation that sparked this I included it anyway. Feel free to disregard if it doesn't quite fit what you are talking about.)
1. As far as running conservation programs for exotic species goes, Australia (as well as New Zealand) may be well-positioned to help species within the Australasia-Pacific region outside of their respective countries, as
@Onychorhynchus coronatus brought up. Papua New Guinea, the Solomon Islands, Fiji, and other Pacific island countries have species of conservation concern and may lack the infrastructural capacities of the two regional powers. Depending on how lax biosecurity laws are for Pacific island endemics, that may be a set of species where Australia could play a major role in a proper conservation program.
2. Even though admittedly it is difficult and expensive for Australian zoos to participate in many international programs for exotic species - and the overall advantages may be small - I think it's worth keeping in mind the idea of seeing captive populations as global, even if they are managed regionally. Australia might make up only a small fraction of the available captive space for species like Francois' Langur, Javan Gibbon, African Painted Dog, and Sumatran Tiger - but these programs nevertheless benefit from the additional space, and one day the survival of highly threatened species like these could be decided on the margins. I'm not personally much of a believer in the idea that most endangered zoo populations will one day replenish the wild, but I also think it's worth it for zoos to maintain their support for the ones they have now so we don't one day end up kicking ourselves for thinking it didn't matter.