While I'm not entirely sure where I stand on this yet, and might potentially be in favour of it, there are a couple of problems that I can see.
Firstly, keeping natives as pets won't necessarily in itself result in better conservation of those in the wild. For instance, the Gouldian finch is very popular and common in captivity, but is still endangered in the wild, with little evidence that the captive stock have had any impact on lessening the problems experienced by those in the wild (though a potential benefit is the large captive stock can be used much more easily for research without having to remove animals from the wild). I can also imagine that being able to keep natives which are currently entirely off-limits could cause problems with poaching - we know how big a problem it is already with our reptiles!
Also, addressing the point brought up in the article linked to earlier of 'genetic diversity is always a good thing': simply put, it's not. Don't get me wrong, a lot of the time it is, but in lots of organisms local populations may be adapted for local conditions, with a particular set of genes which confer a very high level of fitness in that particular environment. Introducing new genes (e.g. from escaped native pets) can then introduce genes which are less advantageous, which can be a serious problem for an animal which already has a small population size.
Not saying that I think keeping native animals as pets is necessarily a bad thing, but there are definitely potential problems which should be addressed.
Oh, also this made me laugh:
A media piece run by the ABC also made some strong arguments against native animals being kept as pets. The piece quoted Dr Karen Viggers and Dr David Lindenmayer, who were deemed to be experts because, like your average bushwalker, they had "experience in wildlife biology and conservation. (3)"
Oh..oh yes, of course, the average bushwalker has the same knowledge of and experience with biology and conservation as
David freaking Lindenmayer, who is only
Australia's foremost conservation biologist.
EDIT: lol only just noticed how old this thread is!