Presumably this is the length of some discretisation of the curve, perhaps one of millimeter-long line segments. (The exact length is uncomputable!) Really cool though!
Yeah, one could draw a tight spiral in any of the open spaces of unbounded length. But "discretization" is probably a good angle to interpret it, since such a counterexample would be discretized to a point.
Well, it doesn't in theory, but it does in practice. Natural phenomena are only fractal over a certain range of scales. Outside that range they follow normal rules.
