> It seems to me that ecological pressure from Humans is the parsimonious explanation.
Humans are very crafty at using the whole animal so the processing of a carcass tends to leave traces all over a settlement wherever bits get used (bone tools and whatnot).
Hunting big and necessarily rare game has a worse risk/reward tradeoff and is less efficient than optimizing for shaking an antelope/deer/elk on the regular.
The environment was being turned upside down in all sorts of places at the end of the last ice age. Humans in many cases where the did hunt things only accelerated the inevitable by a few thousand years which sounds like a lot but is the blink of an eye in terms of evolution.
Basically unless humans left evidence indicating they habitually hunted these animals it's a pretty fair bet they did so only in an occasional opportunistic manner.
"But the cave art" you say?
Nobody posts the 100th medium sized whitetail doe they got that year on social. But if me and the boys get capitalize on a once or twice in a career opportunity to bag a rhino you can bet that mofo is going on the 'gram. Simply put, rare and exceptional events get proportionately more documentation effort put into them. If you "read the docs" that any civilization has left important people and exceptional events dominate when in reality the bulk of the labor was spent on food shelter and clothing.
>The last major landmasses to be settled by humans were Madagascar and New Zealand...
Comparing the ecological impact of the relatively population dense cultures that settled these islands to the ecological impact of nomadic neolithic people (who would have hunted steppe mammals) is like comparing a skid steer to a mining shovel. Furthermore, islands tend to exacerbate the impact because they're a relatively closed system compared to the mainland where if you can't find enough to hunt and gather you pack up and move.