I'm looking at all that's being said about reasons, and it's looking to me like the only options are right after the Civil War, or at some point when a truly despised president or series of presidents gets elected, and the poeple of the USA are mad enough to force their leaders to actually listen to them. Both options seem rather hard to pull off.
Or perhaps
before the Civil War, had the South been more far-sighted.
It is one of history's little jokes that the Electoral College system was adopted in large part to benefit the South, but that when the chips were down. in 1856 and 1860, they would probably have fared better with a straight popular vote.
There would be no way for either Fremont or Lincoln to win a majority of such a vote. Lincoln would have a plurality if the votes remained as OTL, but in this situation neither Breckenridge nor Bell would stand an earthly, and much of their support would probably switch to Douglas, who would very likely top the poll even if there were no provision for a runoff.