"They would have discovered that some of the same traits are shared by these people, like hard work and risk taking. This tells me that the unique trait that the millionaires had in common was mostly luck."

The conclusion doesn't follow. Sharing some isn't the same as sharing all. And, even if they did share all of the measured traits, that doesn't tell us that there weren't unmeasured traits that distinguished the two groups. (Of course, if the difference is in the unmeasured traits, copying only the measured traits may not help.)