I expect you're right about the depth of the till, but it has more to do with than just the roots. Healthy soil is a living ecosystem, and tearing it up wreaks havoc on that ecosystem. To deal with that, we apply synthetic nutrients, which do feed the plants in the short term, but the soil continues to degrade over time, requiring ever increasing quantities of chemical inputs. It's not a good situation over the long term, and it doesn't take a super computer to figure that out.