It is possible that chaotic trajectories that do tap into quantum level indeterminism are confined to such small levels that the macroscopic world is not affected. Diffusion of molecules in a gas in one prime example. In response to i above, the diffusion in stated example has effects orders of magnitude less that macro-level air currents, which we know as chaotic. Point ii above, along with other cases, suggests that even if a phenomenon can be isolated from some form of quantum indeterminacy, this indeterminacy threatens from other directions. Point iii above makes pervasive macro-level indeterminacy likely.
Intuition seems to rebel at the notion of sensitivity to initial conditions.
Our intuitions spring from familiarity with stable systems. Our intuitions are also often untested and held in ignorance. One example of this sensitivity are the liquid bubble chambers physicists use to capture the path of quantum particles. A comparable system with which to compare the results. Measuring equipment to capture the evolution of these perturbations.