Nerudite, the article that I linked to was about an island (Kangaroo Island). Koalas are dying off on the mainland due to habitat desctruction.
One of the problems with a cull is the effect it can have on the remaining population. Starvation is a tragedy but it is natural. A cull is a large scale hunt. In some country in Africa, they had a cull policy with elephants. Well, one of the issues is "what do you do with the bodies?" They decided to not leave them to rot and ... made canned elephant. So then you have a factory (and a market) which now wants a constant supply. It is not too different from the research cited in "Diet for a Small Planet": anyplace the U.S. sends famine aid ends up worse off because we import typical American foods, people develop a taste for the American diet (which cannot be sustainably grown locally and which the poorest families cannot afford) and we leave our cultural imprint in our wake, with serious negative consequences.
They also found that the elephants were terrified of the sound of helicopters (the means by which they did the cull -- shooting them from the air). And it can have terrible social consequences because humans make arbitrary decisions about "who" gets to live. With the elephants, naturally, the humans decided to kill off the old and leave viable young animals. This lead to a generation of adolescent animals growing up without adults to guide them. They began having issues they never had before. Think "Lord of the Flies". The adolescent animals became the elephant equivalent of "gang members". You had elephants getting injured by run-ins with hippos (hippos have wicked fangs and are one of the few animals really equipped to seriously harm an elephant) and stuff like that -- things previously unheard of. Elephants have a very sophisticated social structure and are highly intelligent. Human inteference had a lot of unexpected consequences.
The elephant expert that got hired (perhaps in a different country) -- someone sympathetic to the elephants, someone who had studied them for years and who was brought in to deal humanely with the situation -- had to deal with hunts when a rogue elephant was wreaking havoc on some poor village. But she found methods to make sure they killed the actual rogue and not whatever elephant they came across that happened to be in the area. I believe she concluded that, in cases of drought or other causes of famine, leaving the animals to starve was more humane and less damaging to the elephant population. Starvation was something they understood. Having hunters come in on top of being in the midst of starving was cruel.
Basically, I don't think there are any easy answers. But it makes me think of the Sunset Zoo in Manhattan, Kansas and its little grove of bamboo. They were trying to grow their own local supply of bamboo for the red pandas (which are much smaller than the ones most of us are familiar with). Perhaps someone will create a preserve or begin growing the specialized kind of tree koalas eat and then you could import koalas when you have a situation like this. Habitat destruction is a huge problem and is one of the biggest threats to any animal species.
The problem with a cull is that it sets a precedent with all kinds of unintended consequences. And I am glad they are reintroducing wolves to some parts of the U.S. where they have been "extinct" in recent years.