If the Electoral College was made up of members, who vote how their individual Congressional Districts voted, we would really see the Presidency reflect the wishes of American Voters at the time of the Presidential Election.
I believe this is what the Founding Fathers intended prior to the development of political parties.
The House of Representatives reflects the public’s will. It's called the People's House. Each member was elected in their Congressional District, and represent approximately 700,000 people. The only case where the President would be a different party than the House Majority, would be when the President was not following the interest of the public and they voted against the Presidential Candidate despite voting their party for House.
The other scenario (President not same party as majority of House) would be if the two Electoral Votes per state (that were intended to represent the state's interest) were cast according to the statewide popular vote, or split. In this case Trump,as the Republican Nominee would have started out with the prospect of 300 Electoral Votes (Combined Republican House and Senate Membership) prior to the election. Elections would be Nationwide, not concentrated in large metropolitan areas where voter fraud can be conducted easily. We need to separate National Elections from State and Local Elections. Set up Nationwide Guidelines for Federal Elections, and we need to establish one National Voters Day Holiday for voting. Citizens are being disenfranchised under the current system. As Donald Trump said, It's Rigged."