I don't think "empathy" and "morality" are fundamentally required; rather, they are convenient heuristics for interacting with other humans. As long as you are rational, then acting without empathy or morals would still result in similar behavior (depending on how "smart" and well-informed you are, I guess).

A rational agent seeks to maximize utility. It turns out that murdering people for their organs does not maximize utility! At the very least, society is cleverly structured in a way that the probable utility of murdering somebody for their organs is relatively low.

Basically, my point is that your argument is a straw man. The issue isn't too much logic but rather than you (the agent killing everybody in the example) did not use enough of it. For some reason, all the "arguments" about the inferiority of logic always assume the logical person is extremely short-sighted or ill-informed.