Recently I read an article in which someone pointed out that while compaction in the root zone can be mitigated by better management practices, compaction at the bottom or below this are will remain until the next glaciation period.
That is very, very bad. Practically our only option at that point is to build soil up which is not something modern farming remembers how to do.
Tillage combined with fertilizer. Tilling fluffs up the soil temporarily, but it can and often does compact down harder than it was before.
Organic farming started down this path, but semantic diffusion killed that, and the mantle was taken up by the no-till and permaculture people, after their own fashions.
The question of whether animals help or hinder is still a bit of an open one, but there is some evidence that in the wild, herd grazing was a net benefit to prairie health specifically because predator pressure keeps the herd moving. We see a similar thing in forest settings. In areas where wolves have been removed, the deer end up damaging the trees.
A number of farmers have been working on rotation grazing strategies, typically using movable electric fences and short intervals between moving the animals. Joel Salatin and Gabe Brown are two people you can find on youtube (and in Gabe's case, at the book store). IMO Gabe's videos have more information, while Joel's a better salesman.
Edit to add: There's also controlled fires, but that's a far tougher sell in this day and age.
You can contact your local ag university. Building soil up is hard, if you are building a mm of soil every few years you are doing great - good luck measuring that.
Other posters have mentioned no-till: it takes about 7 years from the time you decide to go no-till until the time when your land yields as much as equivalent land that has been tilled all along (assuming all else is the same), but after those 7 years no-till yields better than tilling the land. Thus the question is are you willing to make that investment.
Search for “regenerative agriculture” and “permaculture“. It’s not necessarily something we “lost”. While some ancient farming techniques can be regenerative, exploitative practices have been part of agriculture since its inception. In its modern form, industrialized agriculture is essentially strip mining.
Symbiotic relationships take things from the other party, but they are repaid in kind.
We can't live without eating things, and in our turn we are eaten. That's life. 'Extract' can have a connotation similar to 'exploit' and if you hear anyone talking about 'extractive' in reference to the environment, that's usually the connotation the speaker is after. But 'exploit' and 'extract' can also mean something closer to 'leverage', which I think is generally the sense one associates with a symbiotic relationship.
My read on this is that humans get a bad rap because so much of recorded history and popular culture is colonial, and the most efficient conquerors also conquered the land, not just the people. Annual plants transport well, and transplant well. A civilization that survives on walnuts or figs or dates or fish can take land from another tribe and thrive immediately, because neighboring tribes have pretty similar diets and agriculture. But conquering another civilization? More efficient if you can bring your agriculture with you, destroy theirs, and replace it with yours. Even if you leave, that scar will last for generations.
Conquest is less effective if you have to assimilate first. Which is not to say that it doesn't work (eg, the Americas) but your competition might get there first. The people with attachment to place were better stewards, but that attachment makes you vulnerable in other ways.
That is very, very bad. Practically our only option at that point is to build soil up which is not something modern farming remembers how to do.