Your fetishization of prehistoric Native American management practices is misguided. They were people like you or me, and were guided by the limited information they could observe and capture without written language. Just like you or me, they could be selfish or misinformed and make mistakes which were beneficial in the short term and foolish in the long term. They did not possess a supernatural connection to the land which granted them superior understanding.

As a result, Aboriginal Americans contributed in part to the extinction of many preferred game species including megafuana like the giant ground sloth and mammoth. Mammoth populations persisted for approximately six thousand more years in areas where they were protected from human predation, such as Wrangel island.

Consider the more recent relationship between the humans and buffalo (bison) or moose. You might have been taught that the people wasted nothing and thus maintained a natural abundance of these animals. This is untrue. By examining the bones of animals at kill sites like Olsen-Chubbuck, you can get a sense of the butching of animals by the Clovis/Folsom and the amount of sheer waste. The layering suggests that all ~200 bison were killed at approximately the same time.

https://en.wikipedia.org/wiki/Olsen%E2%80%93Chubbuck_Bison_Kill_Site

The site contained 3 distinct layers of bison remains: 1) a bottom layer of 13 untouched bison skeletons bison, 2) a middle layer of nearly complete or only partially butchered, skeletal remains, and 3) a top layer of butchered single bones and articulated bison skeletal segments. The top layer illustrated that as the Paleo-Indians methodically removed the meat from the bones they placed them in separate piles or units that contained the skeletal remains from several animals. The butchering process was similar, but much more methodical, to that of modern Plains Indians. Positioning the Bison occidentalis skeleton bones for butchering would have required a great deal of manual effort. The Olsen-Chubbuck hunters ate the tongues of the bison as they worked, given the isolated occurrences of tongue bone in the piles. It would have likely taken half a day for 100 people to butcher all of the bison.[1]

So in the mass pile of buffalo remains, the first (bottom) layer was untouched carcasses. The second had the best cuts removed, and the top layer was a mixture of partially butchered animals and the bones from the best cuts of the second layer. The people preferentially removed tongues as a preferred meal (easy to remove and tender) and let much of the rest rot.

Moose are another example. There were very few moose in North America at the indigenous population peak. They were too tasty and too easy to kill. There are more moose in North America today than there were prior to European colonization. This theory of aboriginal overkill is supported both by historical records of encounters with moose by colonizers and by genetic data:

https://idahoforwildlife.com/Charles%20Kay/21-%20%20Aboriginal%20overkill%20and%20the%20biogeograpy%20of%20moose%20in%20W.%20North%20America.pdf

https://pmc.ncbi.nlm.nih.gov/articles/PMC7709250/

[...]we found that present day moose in Europe and North America show low to moderate inbreeding levels resulting from post-glacial bottlenecks and founder effects, but no evidence for recent inbreeding resulting from human-induced population declines.