In most of this footage you will see that there is a small mass of workpiece material (Built Up Edge or BUE) that is doing the “penetration.”
The fracturing ahead of the tool, and the occassional jamming of material under the tool, and the waviness of the generated surface are concepts to keep in mind when you try to understand why you are getting the finish on the surface that you get.
Also, a good way to visualize how the material is being workhardened by “rubbing” where the material is not separating easily ahead of the tool.
The cutting edge can run at around 1000°F, which is part of the reason that the extreme temper resistance of high-speed steel is so valuable. In addition, the coolant gets completely squeezed out from this region, so the extreme pressure additives fulfill the essential role of providing a solid lubricant.