My strong suspicion, and we know how much suspicions are worth in science, is that many if not most of these creatures would indeed have survived the end of the ice age were it not for the influence of man. I say this for the simple reason that the ice ages as a whole was a period of glaciations and inter-glaciations. The latter periods were as warm, and often much warmer, than the current era. Yet, while there was a typical turnover of species, there were no mass extinction of animals larger than 50 or 100 kg, as we saw in the Pleistocene/Holocene. This event seems peculiar to this inter-glaciation. And it seems, coincidentally, to correspond roughly to the arrival of humans in each of the major regions of the world. Why should Australia's extinctions be 50,000 years ago, well into the last ice age, while North America's be 11,000 years ago at the end? Perhaps because those dates are when humans first arrived in both continents. There's no smoking gun
per se, but there's smoke. Quite a bit of smoke.
In the case of Australia, that smoke may be due to the fires that aboriginal people set in the bush, which may have altered the ecology of the outback enough to cause an extinction cascade. A cascade which has left Australia bereft of indigenous large animals, with the exceptions of red and gray kangaroos. In other words, anthropogenic influences beyond mere over-hunting might have contributed to these mass extinctions.