Horrigan is a different man than Callahan—more open, more talkative, more romantic. In short, he is more human and not mythic. Sure, there are some similarities—they are both world-weary loners frustrated by the brass—but there are more differences.
Besides, there was no way to mesh the two characters' histories. So Callahan would have started out as a Secret Service agent, then headed to San Francisco after the JFK assassination in 1963 to become a homicide inspector, and then sometime around 1990, when he was turning sixty, he would have headed back to Washington, DC, to become a Secret Service agent again? That trajectory would have made no sense, and the Dirty Harry identity would have totally distracted from the rest of the material.