What are the benefits to the US Electoral College system?

Like most weird things with the American federal government, you have to remember that at the founding, the individual states were much more autonomous, more similar to individual countries than they are now.

Primarily, the electoral college was one of many compromises made between the states so that all of them would sign on and join the union. It was deliberately designed to give smaller states a disproportionate say in the presidential election, to sooth their fears that they would end up being controlled by the larger more populous states (again, at the time, people would have identified much more strongly with their state than with the federal union.) So, the benefit was that it gave the smaller states enough of a say that they were willing to join the union.

If you conceive of the United States as a single nation state, which many today do, but was not historically a universal norm, then there's no real benefit and only serves to help Republicans maintain power, since less populous states tend to vote Republican. This is what most people tend to believe, especially people on the left, and why you largely see most people online oppose the electoral college.

If you conceive of these United States as a group of states and not just a giant nation state, then the electoral college allows the separate states some hedge against being dominated by their larger neighbors. Almost no one actually believes this. You'll mostly see Republicans bring up this argument, but by and large they're hypocritical about it(they'll use states rights when it serves them, and federal power when convenient). There are some people who do truly think that the states should be left to govern themselves, as a matter of principle and not just as part of a political game to get their way when convenient, but they are very rare.