Why are sharp tools important?

It seems fairly obvious that sharp tools are necessary to be successful at woodturning, and very often a dull tool, or at least one that is not as sharp as it should be, is the reason for bad experiences. But have you ever considered why? I would like to suggest three reasons, though there may be others that I haven't identified yet.

1. The most obvious is that a sharp tool will cut the wood cleaner. The wood fibers are more likely to be cleanly sliced by a keen edge than a dull one.
2. A sharp edge can pick up a fine cut. A section through a sharp edge looks like two surfaces coming together at a fine point which is capable of removing fine shavings. When the tool becomes dull, that fine point becomes rounded off, and can only pick up a cut that is thicker than the rounded edge.
3. A smaller force is needed to push a sharp tool through wood. There is an equal and opposite reaction, the rotating wood trying all the time to throw the tool backwards. A dull tool will see a larger backwards force, and will be harder to control.

Item three is perhaps the most important. A tool that is difficult to control may not cut in the direction you want it too, making it difficult to refine the shape of fine curves. If you have to push the tool forwards, you may just end up pushing it up and over the wood you are trying to cut. And if the wood succeeds in pushing the cutting edge backwards, the bevel may lift off the surface and a catch may result.