This notion of morality is a perfectly logical assumption, befitting the confines of atheist philosophy.
But there is a problem with this atheistic vision of goodness and morality. Strictly speaking, goodness and morality are not rational in the atheist conception - they are innate drives within human beings.
Human beings are rational, and can and do come to the conclusion that morality goes against their own self-interest.
Unlike other animals, human beings are rational beings – or at the very least, possess the capacity for reason to a degree which other animals do not. Humans also naturally seek what is in their best interest.
But moral behavior often goes against human self-interest, because morality often consists of imposed limits on a man's autonomy and material improvement. For example, a moral man would not steal or sleep with another man's wife, even if presented with the opportunity.
But fulfilling one's self-interest means the betterment of oneself, not necessarily the betterment of others. Logically, if good and evil are merely mental constructs, personal obedience to moral statutes becomes folly if obedience to those statutes is not in one’s self-interest.
Intelligent individuals realize that without a God, obedience to any moral code is folly, and that good and evil are often mental constructs designed by weak individuals to restrict the predatory nature of the strong. Accordingly, if a powerful individual successfully avoids or rejects the confines of morality to gain power, then he (or she) has nothing to stop him from seeking his own self-interest at the expense of others.
Powerful individuals who reject the notion of God believe they have have no check on their actions, because there is no being or higher power to punish them for seeking their own self-interest at the expense of others.
This problem is reflected in the lives of several atheistic individuals who attained power. Joseph Stalin, Pol Pot, Mao Zedong, Mussolini – all of these leaders were atheists who set themselves above the chains of morality, with disastrous results.
The problem with atheist morality isn't that evolution precludes morality. The problem is that atheistic human beings are sometimes too rational and too self-interested to submit to the innate human drive for morality.