They should eradicate the electoral college, but there is another fix I'd sooner see.
Plurality voting (whichever candidate gets the most votes wins) gives a very strong push towards two party elections. In any contest, if your favourite candidate is not one of the top two, you're better off voting for whichever of the top two is best (or least evil), because a vote for your favourite will be wasted. Even if a candidate is the favourite of 60% of the electorate, if they are perceived by the electorate as not being one of the top two, they'll receive few votes.
With preferential voting, you rank the candidates. You can rank your favourite first, and if it still comes down to the two major party candidates, your ranking between those two will carry just as much weight as party faithful who put one of the major candidates at #1.
This allows compromise/centrist candidates to win, and allows for new coalitions of interests. For example, in the USA currently the evangelical Christians and those favouring small government have found a home in the Republican party, but these two interests have no essential alignment. (That many believe both or oppose both is partly an artefact of the current two party system - if you turn up to Republican rallies because you're evangelical, you'll get bombarded with small government arguments, and you'll want to feel part of the group.) Currently an evangelical who wants to increase social services spending has no chance of election (neither major party will take them as a candidate), but with preferential voting they do.
The partisan divide in the USA has become toxic. Preferential voting can erode that divide.
For electing a single candidate, I suggest using a Condorcet method. For multi member constituencies, the single transferable vote works well. In either case, it may be useful to have a prior round of primary voting to keep the number of candidates in the preferential voting round manageable.
Major parties could chose to put up multiple candidates. Imagine a Trump/Cruz/Rubio/Clinton/Sanders election. I believe such an election would have had a different outcome, and that the electorate would be happier with the outcome.