In 1868, when the Fourteenth Amendment (including its Section 3) was adopted, presidential elections looked something like this: Political parties gathered together in a convention to nominate candidates for president and vice president. State parties would then choose presidential electors inclined to support these candidates. The state parties would then print tickets in each states that typically listed these candidates and a list of presidential electors who would support those candidates. (Voters could “scratch” electors names if they did not support the entire ticket.) State election officials would tabulate the votes cast for each elector, and the highest vote-getters (ranging from 3 to 33 electors, depending on the state at that time) would be elected. The electors would meet sometime after election day to vote for president and vice president. Congress would then count the votes and declare a winner.
The only place in this process where an adjudication of a candidate’s eligibility might formally occur would be in Congress (which, in 1868, hadn’t yet ever occurred, even though it had been discussed as early as 1800). (It could also occur in the nominating convention, among voters, and among presidential electors.)
Now, of course, since 1868, much has changed, as I chronicled earlier on the power of states to adjudicate qualifications. Today, states print the ballot and develop rules for who appears on the ballot. Most states administer primary elections for delegates to a convention to choose the party’s nominees. States prohibit “scratches” and require voting for all electors as a bloc in all states. States do not even list the electors on the ballot in most states and instead only list the presidential and vice presidential nominees. States often require electors to pledge to support the ticket, going so far in some states as to replace electors who attempt to vote for someone else.
These developments make the application of Section 3 to contemporary presidential elections (setting aside any of the disputes or discussions about Section 3 itself) something of an issue of translation. The state has much more direct involvement and control over elements of the presidential election–the primary, the general, and the electors. I think that’s permissible under Article II and the Twelfth Amendment. But it doesn’t easily translate to other contexts of the administration of presidential elections, including the application of Section 3.
This isn’t to say it can or cannot be done, or that it should or should not be done. It’s only to say that some of the debates of where we are today are anachronistic. The mechanisms we use today were not available in 1868, and those newer mechanisms create some translation complexities in the present age–for which I offer no easy answers, simply this observation.