In a nutshell, once a simple majority (>50%) of US states enact it, they will have all electoral votes for presidential elections awarded to whichever candidate gains most votes. That means the Electoral College's effects (faithless electors, not aligning with popular votes, etc.) will be sidelined.
Therefore, rather than an oligarchy (the Electoral College), it is the public that decides the election.
Situations like Bush winning or Hillary losing, would then no longer occur, because both of these won only due to the electoral college.