The EC was a compromise. No one liked it, but as Prof. Beeman says, the Founders agreed to the EC “grudgingly and out of a sense of desperation, as the least problematic of the alternatives before them.” There were a lot of competing interests at play, and the EC cut the Gordian knot in a way no one liked but everyone could live with.
Over time, a lot has changed, so it is certainly possible that the EC has obsolesced. In my view, however, it has not obsolesced but has instead remains a remarkably stable and elegant solution, adjusting the competing economic interests of high-density and low-density populations. If the Convention were held today, is there any chance that the farmers and ranchers would agree to a popular election of the President? Of course, not. We would end up with some system that protects the lambs from voting with a majority of lions on what’s for dinner. It would probably look something like the EC.
BTW, I can’t find any evidence of the South Carolina delegation’s view on election of the President. Can you point to it?