The science of physics is an attempt to understand
All of Reality, which is generally considered to be an even larger set of phenomena than your description of economics

Are you suggesting that since we can never
really understand All of Reality, that no 'hard science' of physics can exist, and that such a purported 'hard science' of physics can't have any predictive power or utility?
Physics does not want to understand all the universe. It only wants to understands how its parts work, and generally limits itself to the smallest and simplest parts.
Phisicists may study the behavior of isolated atoms of generic bonds between atoms, but if you ask them to predict what a dozen atoms will do when they get together, they will tell you "sorry that's Chemistry, not Phisics". Ditto if you want to predict tomorrow's weather, create a better strain of wheat, cook a good meal, pick up a girl at the bar...
And even the simplest "economic atoms" are already way more complicated than a tropical storm...
You seem to think it is somehow not 'hard science' to study dynamic nonlinear systems, and that no good can come of such study. I don't know why you think that, but I'm pretty sure a vast array of scientists, from meteorologists to mathematicians to quantum cosmologists would strongly disagree with you.
You answer does not address whether it is possible that there might exist a hard science of economics, as opposed to a mere philosophy, which was the original point. Characterizing economics as a dynamic nonlinear system (which it certainly is), does not invalidate it as a subject of hard science.