The reason nations like the United States and Canada have a Republic (Roman), a Democracy (Greek), and Figurehead Representative as the President or Prime Minister, is because the American founding fathers found it best to study the history of other great nations, and even bad ones, before founding their own.
Even though Americans abhorrence for monarchies is well known, having a president goes back to the ancient times of Kings and having someone to see to as a leader, and/or blame as a failure, which Rome did not have from Romulus 700B.C. to Caesar 36B.C.