Ah, but which proportion of all existing systems are chaotic? And of those that are, how chaotic are they? To what degree can you still extract predictable properties from chaotic systems? The Wikipedia page on chaos theory says that

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices. Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations. Everyday examples of chaotic systems include weather and climate.

but we still have useful models on all of those systems, even though they're imperfect. Whether the models are useful enough depends on what we try do with them, and how accurate results we need. Chaos theory is evidence in favor of my friend's intuition, to be certain, but it doesn't seem to resolve the question by itself. A comprehensive review of different systems and phenomena and the limits of how well they can be modeled could go a long way in that direction, though. Anybody know of one?