I am not an expert on this literature, but I do know that close elections are a problem. I also believe (perhaps wrongly) that independent election administration is self-enforcing when it emerges from and exists alongside multiparty competition. If right, this strikes me as a way to design other institutions so that they enjoy broad legitimacy.
The unit-rule allocation of Electors is therefore an issue: first by constraining the number of parties, second by making outcomes depend on very small numbers of votes.
Here is an idea for the sake of argument: mandate closed-list PR within states for choosing Electors, and move the election of the President into the Electoral College.* Make it negotiate and produce a coalition. Do what the Framers intended, except in a more modern way.
I do not think this change is likely, but it’s interesting to think about.
*The EC already chooses the president in a technical sense, but it does not deliberate. Hence the notion of a “faithless elector.”