You’re right, the Great Plains are just a big, flat seemingly endess slab of land (actually, the vista of flatness extending for hundreds of miles IS dramatic, in an understated sort of way… ) But you don’t need a lot of cliffs - just enough cliffs. Rivers like the Mississippi, Missouri, Illinois, and forth are bordered by cliffs that are tall enough to kill if you fall off (and there are state parks in the Great Plains that have a number of tourists fall off cliffs and die every year)
Prior to the (re)arrival of the horse in North America, the plains tribes did not live year round on the open prarie - they hung around the edges where timber and wild foods suitable for humans were more readily available, or traveled in the river valleys where, again, there was timber and people food as opposed to horse or bison food. So there were vast tracts of land where people seldom if ever went, and in those areas the buffalo were seldom hunted by humans.
During that time period, yes, the natives DID run herds off cliffs. A buffalo is a big, dangerous and aggressive animal. You could either try to sneak up on one - and hope that it doesn’t see you first and charge, or that the herd doesn’t turn on you, then worry about wolves and coyotes challenging you for the kill - or take adbantage of a stampede. It’s not that they wanted to destory more than they could use, it’s just that it’s a heck of a lot safer, on average, to run a bunch off a cliff than to pick them off one-by-one on foot. The resulting pile up not only provided the natives with more than enough for their needs, but also led to a feast for the local predators/scavengers who would happily go for the easy pickin’s rather than challenging an armed human for dinner.
When the plains tribes acquired the horse it allowed them to exploit the open prarie - they now had the means to travel long distances and haul the plant foodstuffs, timber, and other items they required the necessary distances. They no longer needed to run herds off a cliff - they could use horses to drive a buffalo off from the main herd and kill it. They could transport meat and other animal parts farther and faster, and in greater quantities.
So there were fewer “buffalo-jumps”, but with the high praries opened up for human exploitation probably just as many animals were killed. The buffalo lost their human-free refuges.
The natives weren’t too proud to take advantage of the dead and dying left by a natural stampede, as well.
It had little to do with being “in tune with nature” or mystical mumbo-jumbo - it was a matter of the most efficient way to keep yourself fed in a harsh environment, with the least physical risk to yourself (they didn’t have trauma centers back then). Same reason the natives liked guns - sooooo much easier to kill the buffalo from a distance, minimizing your chances of being gored or trampled.
When there was an over-abundance of a resource, when there were more dead buffalo than the tribe could possily use and/or preserve - yeah, they took their favorite bits and left the rest to rot. Because they didn’t have much choice. You can carry only so much pemmican and buffalo jerky. Conversely, when times were hard they ate everything - and there were times of famine on the Great Plains. These folks were at the mercy of their environment much more than we are right now.
Would the Plains Tribes have driven the buffalo to extinction in time, even without the arrival of the Europeans? That I don’t know - the environment itself was pretty darn harsh and killed quite a few. I’m most famillar with the tallgrass prarie environment in Indiana and Illinois, and even today it can get pretty nasty. Temperatures range from 40 C in the summer to -35 C in the winter. Winds range from calm up to 115 kph (and the winds can get that high even in a cloudless sky - we call it a “windstorm”) More tornadoes than anywhere else on Earth. Very little natural shelter - it’s flat land, after all. River valleys flood in the spring. In summer some years you have a lot of rain, some years it may not rain for two months. On the eastern praries, the grass grows over 2 meters tall - try navigating through that when you’re on foot! Even from horseback, the vegetation may exceed the height of a tall man. Further west, in the shortgrass prarie, obtaining water may be almost as difficult as doing so in a desert. Although there are some edible prarie plants, most of the vegation is inedible to humans or edible items present only in small amounts. The Plains Tribes had a meat heavy diet because there wasn’t a lot else out there to eat. Sure, there were rabbits and birds - but running down a rabbit yields little meat for the effort, and birds are hard to catch without nets. Tribes really deep into the Plains had to trade for the tent poles for their tipis, flint or obsidian to tip their arrows, plants for food and dyes and medicines.
Out on the Plains, natives froze to death in winter, died of heat stroke in summer, drowned in rivers, were carried away by tornadoes, struck by lightning, probably got caught by an occassional grassfire, trampled in stampedes, attacked by predators (wolves, bears, the big cats), broke legs and arms, some years starved to death (in really bad winters the elders were “encouraged” to go for long walks in blizzards), and that’s not even considering diseases. Before the Europeans showed up the natives didn’t have a lot of diseases and plagues were largely unknown. There is some evidence that the Plains tribes suffered large die-offs from European diseases transmitted along trade routes from Central America before they ever saw whites.
In short, the low technology of the tribes limited the damage they could do, and natural hazards limited their numbers. With the arrival of European “crowd” diseases, their numbers would be further limited for quite some time to come. So even if they would have eventually driven the bison to the brink of extinction it would have taken many more centuries than it actually did with the arrival of the white man.