The best reason is protection from vote fraud. Consider what could happen under the following three approaches:
A) System as is now, states run elections and we use representative Electoral College.
B) States run elections as now, but we use the "popular vote"
C) Federal government runs a popular vote election.
Now if we go with option C and some partisan group in power is able to rig the election process to keep themselves in power, then we are lost.
If we go with system B its even worse. We are almost guaranteed the process will be corrupted in a competitive way by the most partisan state governments. For example say Texas gets sick of California padding their totals with dead people and illegal aliens and starts getting very "liberal" in how they count votes. California gets mad and gets even more "liberal" in how they count votes. In short order you have competitive vote padding and at some point or another it will be clear to all that the totals are no longer even plausible....perhaps Rhode Island will suddenly report 3 billion votes for some local hero of their own after the other state's inflated totals are officially reported...and then perhaps the states will compete to be the last to report their official totals....like a second before midnight on January 19th...
Best to stick with system A. yes California and New York can count dead people and illegal aliens, but the Democrats have to corrupt the less partisan swing state's election processes in order to win...and that is harder to do. No matter how "liberal" they are in counting votes, they only get so many EC votes.
If liberals keep yapping about wanting "one person one vote" though, we can always compromise with "one county one vote" ;-).
Can you imagine somebody wanting a recount in all 50 states and DC? Popular vote system would do that.
California will just make every person a county!