The primary advantage of the electoral college is that in the event of a recount, the recount is held only in the States that are close.
A secondary advantage is that it does not require there to be a Federally imposed uniformity on voter registration requirements and the like.
A tertiary advantage is that in the event that a locality engages in vote fraud, the damage caused by that is limited, altho that is offset by the fact that a smaller degree of fraud in certain close States might have an effect. Still, we certainly don't have to worry that vote fraud in Utah in DC will affect the presidential election anytime soon under the electoral college.
In other words, fraud capacities can be moved to where they matter, as the GOP demonstrated in 2000.