> I have a hard time believing that hunter gathers in tiny tribes traveling on foot with primitive weapons could have hunted and wiped out entire species of large animals from continents
One thing humans could was starting fires that would drive many animals into a designated killbox, among other ways of "cheating". Humans were uniquely capable (at this size scale, at least) to both hunt species in excess to their need and cause outsized damage to their habitat in the process.
The default is to outpace your need. Imagine if we evolved to somehow hunt just enough meat. There’d be some of us with less efficient systems for controlling that behavior that end up starving while they think they are bringing in enough food. Thats no good for reproductive fitness. Overshooting on the other hand is good.
Another factor, symbiotic relationships tend take much longer to evolve that carefully balanced relationship between symbiont and symbiont. Parasitic relationships tend to evolve sooner and its also not uncommon the parasite overshoots and kills off its own host.
One thing humans could was starting fires that would drive many animals into a designated killbox, among other ways of "cheating". Humans were uniquely capable (at this size scale, at least) to both hunt species in excess to their need and cause outsized damage to their habitat in the process.