There is some truth in parts of what you say but its still a highly biased view point. Firstly the relatively small size of the Native American population made all that land management easy.
Before the Spanish showed up with many fun new diseases, their population was up to at least 50 million, if not 100 million or more. It was smaller than what we have now, but not as small as people think.
Simply burying your shit works when you only have a handful of people living on a large acreage. That does not hold up when your numbers get much larger.
If they get much larger you have to actively compost the crap, sure.
"The flyover states" are also "America's bread basket" they are not empty.
Actually, most of the food comes from California.
They do have a good deal of forest, more than they once did
Forested area is nice, but forest biomass is what really matters, because old trees fix more carbon (and so on) than new trees covering the same area.
The rest of space is very much being used to group the wheat and corn that went into your breakfast cereal this morning.
Stuff we should be eating less of. Actually, I'm eating oats. 40% of our corn goes to make ethanol and 4.7% for HFCS. Only about 50% of the land is actually used for crops, and if we cut the HFCS out of corn we could save approximately 27 million acres there alone.