The other replies make fair points, but tillage does still have it's uses.

Quick examples:

  - Inversion tillage (ploughing) to bury green manure crops or bulky organic manure
  - Subsoiling (deep tillage) can help break underground compaction, to allow better root penetration
  - Working with soils prone to surface capping

  - Full inversion tillage
  - Low/min-till
  - No-till

EDIT: This is a response to the question "why do it?" rather than anything in the context of the article itself.

This is actual reality. No-till is great until you have to till because of circumstances. Sometimes what happens needs to be dealt with; we've had years of heavy, heavy rain, and despite decades of no-till farming, it still can't absorb limitless water. That's when compaction happens, especially if you need to get crops off wet ground. So you deal with it, and start again building the soil back from tillage. You don't have to always haul out the 3-bottom plow, but even discing has a recovery period. But it's better than trying to seed into concrete.

And tillage can work well by bringing up nutrients. Some crops will do this themselves to an extent, or you can plant forage crops for a time that will bring up nutrients. But subsoiling to break deep compaction or simply bring up phosphorus or potassium from lower levels can breathe new life into a field.