Earlier quoted context omitted.
I can perhaps refine (1) and provide some insight in support of (2). It does make intuitive sense for handles to be 1/3 of the length of the curve, as that makes the "speed" close to constant, but this is not the smoothest possible choice in general. In particular, it's not the best approximation to a circular arc, which by most reasonable definitions is the smoothest possible curve. I did the math[1] and found that…
The ideal dimensionality of the parameter space depends on the jaggedness of the curve. Derivatives are useful when they stay constant over a stretch of time; when derivatives vary too much, it becomes more efficient to use more points of lower degree. This is the same calculation in other domains of approximation: numerical integration, DiffEq, and Taylor series. For example, to draw rough surfaces, point-to-point l…
I usually just draw a quick simple line and tell Illustrator to rough it up for me. There's a lot of ways to do this; "use a custom brush" is a common one, so's "apply the Roughen effect". These will dynamically generate a buttload of virtual points in the vicinity of the basic path when it gets rendered; the editing view is still just a handful of points. Much easier to edit, much faster to draw. If I need precise, human-defined jagginess to a path, then I whip it out with the Pencil, and push it around with stuff like the Puppet Warp tool, which lets me drop a few pins into a complex set of paths, and distort it based on how I move those around.
Illustrator's Pencil tool actually performs a certain amount of smoothing on the raw positional input from the drawing tablet. There's a slider for how much it does this. I have it right in the middle of the range and it makes for a pretty nice compromise between catching every deliberate motion of my fingers/hand/arm across the tablet, and throwing away the little irregularities that I would be working hard to eliminate if I was working in pen and ink.