Many animals not used to humans show no fear of them, and thus were easy to eliminate before they could adapt.
As we have seen from the spread of invasive species (in Australia and elsewhere) a new species tends to throw things out of whack, and they make a huge impact within a short time.
Of course it isn't the sole explanation, and the data is far from conclusive. But the data seems to show that when humans showed up, a lot of mega-fauna soon disappeared.
And it doesn't take “bloodthirsty” or “short-sighted”; it just takes an easily exploited resource and hungry people.
The numbers simply don't add up for me. I take your points but I doubt mammoths were ever "easily exploited" -- ditto dire wolves, sabre-toothed cats, cave bears etc. Ground sloths maybe. I like your Larson cartoon BTW.
While Occam's Razor might indicate your conclusion, in this case there's simply not enough real evidence either way to convince me. I need a whole lot more data about how many hunters there were etc.