The writers of the Constitution did not require a general election for the presidency. According to the Constitution, the state legislatures choose the presidential electors. Starting in the early 19th Century, legislatures began letting the people choose the electors. By 1844, only South Carolina still had the legislature choosing electors, and that ended in 1868.
“According to the Constitution, the state legislatures choose the presidential electors”
I just looked that up. The electors were chosen in each state by popular vote over a five day period.