Yes, there are specific indicaions of us making those same mistakes, here and there, over our existence as a species.

But overall, the "killing off everything else" is the story the great white hunter cutlure tells, gotta keep that in mind. It's what they would have done - and have done! - so it's what they assume everyone did.

If you look at more recent and holistic anthropology, archaeology, etc. last 20-40 years, some of those stories are getting turned upside-down, or at least majorly revised. From Chellis Glendinning "...in recovery from western civilization" to "The Dawn of Everything" and "The Biggest Estate on Earth" and so on.

Just one example - "hunter-gatherer" is backwards - evidence and direct accounts and oral tradition indicates that aboriginal cultures were primarily gatherers and horticulturalists (skilled use of fire to manage landscape is found everywhere there was burnable landscape, along with other indications of advanced horticulture). And most of the gathering and processing was done by women and children. Men went hunting some, sure. But it was supplementary overall, ceremonial sometimes, celebratory sometimes, not primary to the everyday diet in most cases. As always there were exceptions - locations with very long cold seasons would be more hunting-reliant, for example.

And, if you were one of those guys, and had to choose, what would you do? Go after a sabertooth, or a woolly mammoth, or a grizzly-like bear, or some other legendary vicious deadly megafauna? Or, go after any of a great variety of much smaller and easier to snare and slaughter and cook critters?

Let's get real - a relatively tiny global population of 'cave men' killing off most of the megafauna with flint spears etc. is really a bit absurd. And we didn't have the industrial means then to just destroy their habitat like we do recently. But it's what the great white hunter imagines they might have done back then (before they had high power large caliber rifles with scopes), so that's the story they tell.

Dang that got long, I should make it a piece of its own... :-)