I ask this somewhat rhetorically, because the EC is designed in some ways to replace the parliamentary function of selecting the head of government (ie the prime minister). The Founders did not want a British-style parliament and explicitly separated the executive from legislative branches. Nonetheless, they still perceived a body that mirrored the legislature acting as a parliament to select the president - the Electoral College.
Wrong. The Westminster parliamentary system had not quite developed yet when the Constitution was ratified, as the prime minister was still seen as being in service to the king and not to Parliament. They saw the President as substituting for the king and Congress as substituting for Parliament, but added aspects to the system to limit the power of the President and strengthen Congress. We simply diverged from the British system before it moved into a Westminster parliamentary system.