It's a slightly weird question i suppose but why are drills long? Why do they keep being swirly after the start, when it comes to drilling stuff?

When it comes to archimedies screw I understand you want to keep the material (water) continuously pumped upwards. But for drilling in wood? Why? The amount of material displaced could simply be behind the head of the drill and the cutting head could be enough. Right?

Another partially related question, why I've seen in movies (Saw) that they tape the drill head for the sough after drill distance, as she drills the skull of a person. Why/how does that work? Surely, there is not way that the drill wouldn't continue drilling just because the upper ends are taped?