You are correct, of course. Based on the writings of the founders at the time they established the system, it was clear that the system was never intended to be a democratic one in the first place. They didn’t trust each other and they certainly didn’t trust uneducated rural Americans with the power to select the chief executive.
The fact that they couldn’t agree on whether or not to count a slave as a full person for the purposes of counting population is all the more reason the system should have been swept away ages ago.