1) That larger states will be able to control and rule the semi-centralized federal government[1].
2) That a populist local [2] official will get swept into office and rule by decree protected by his voter base back at home. This will block the smaller states from getting there voices heard [3].
3) Founding Fathers knew there was no good way to decide who can vote and who couldn't. So instead they decided to go with actually officials. These would be men who would be educated, elected by the people, knew the issues and...
4) Wouldn't be bound to follow the actual popular vote nor a political party[4]. Founding Fathers didn't like political parties. One of reasons 13 Colonies was so mismanaged was due to the politic appointments done by British Parliament, which was primarily controlled by well British gentry [5]
Mob rule of democracy can only happen in one from of the many different forms of democracy and thats direct democracy. Which I hear Swiss are doing quite well at without lynch mobs or anything. Well okay ever so often the one racist law gets by in area but i don't know enough about Swiss system to talk about it
However there are other forms of democracy which are much better and don't let someone win by just getting 24% of the popular vote (yes this is mathematically possible) or don't have fail rate of 7% (4 elections have had the person with the popular vote lose to someone who won the College)
[1]At this point the United States was more like the EU (before the Euro) then single nation state, each state was even printing and minting its own coinage.
[2] Travel was time consuming most officials and communication networks didn't really exist at this point. No telegram no pony express nothing. You had to wait for someone with news to come to you and tell you what happen
[3]This was major concern during the lead up to the Civil War hence way North and South played a game of national chess on when allowing states into the Union.
[4] Faithless electors was quite common place and even played games political chess to ensure the person they thought deserved the office of President and Vice President (remember there was time where the VP was elected and not appointed)
[5] This is complicated (Seven Year War and couple others things that make Game of Thrones look like Sesame Street) one and kinda falls back to cited point number 2. British government did care, the problem was they had no idea what the fuck was going on till someone got on boat and told them what was going on. For instance the Stamp Act, nullified the second Parliament heard what Grenville did. With good smack down from William Pitt the Elder. Who even commented that the Americas were right to resist and illegal tax.
Thats why it exists. Illegals where never thought when Founding Fathers came up with how to appoint president and vice-president. Yes I said I appoint. Presidents and VPs were never suppose to be elected by the people.