However one may think about the EC - it is definitely more important to get the voting procedure clean! It´s unbearable for the United States that still dead people votes count or that the list of people who are uneligible to vote (like criminals) is hidden from the public in many states. We don´t have these problems in Europe and therefore consider your voting procedure as inferior. You have too many posssibilities to manipulate elections (and I blame the blue and red side for that). I know you will dismiss it, but being registered from birth till death by the city you live in, and bearing a national ID with your address on it has advantages. We receive a notification a few weeks before our election by mail, then we can send it back and ask for a mail vote or we go to the ballots, show our ID or passport, our names on the voter list is marked and we get our vote. When the ballots close, the number of marked names is counted and must be identical with the number of votes. Then the helping hands in the office count the votes - and we take care that at least one of the two big parties is present. With that easy procedure, we never had any claims that there could be a fraud. Oh, and the right to vote can be taken away by a courts decision, but it must be said in the sentence, and for max. 5 years. This (our) system is different to the US -and ... that´s a point why many many people put the finger on you.
In 1993 just after Bill Clinton became President the DemocRATS in Congress forced the "motor voter" bill through. It requires every state to have voter registration at the same places where states issue drivers licenses. Every applicant for a drivers license must be asked whether he or she wants to register to vote too. The problem is the qualifications for voting are different than those for driving. Quite a number of illegal aliens end up being registered to vote this way.
While drivers licenses are used as picture IDs for many purposes, they aren't not usually required to be shown to prove one's ID when voting. In fact quite a few DemocRAT demagogue lawyers file civil rights suits against states and localities that try to require picture IDs as proof of ID. Observers who ask people for IDs are often served with civil rights lawsuits or even physically intimidated. There are a number of precincts in some inner city strongholds that regularly vote 90%+ for DemocRAT candidates where poll watchers are afraid to go for fear of their lives.
Another thing is that different states have different standards for voting, although much less different than 150 years ago. While there have been constitutional amendments mandating suffrage for men over the age of 21, then women, then citizens over the age of 18, etc. there are still differences between states. The states jealously an rightfully guard their prerogatives to determining those policies. Some states ban convicted felons from voting after serving time in prison. Other states allow convicted felons to vote after they have served their sentences. A handful allow felons still in prison to vote. The Electoral College eliminates the incentives for states to competitively lower their standards. If a prisoner is not allowed to vote for president in one state but is in another, the state with lower standards effectively has a larger impact on the election if it is determined by the popular vote. There are some politicians in California who want to lower the voting age to 14. Without the Electoral College, California would be given a bigger voice in the outcome of presidential election due to the expansion of the proportion of the population eligible to vote.
Finally, you should look more closely at the EC institutions. The EC does not elect it's president by popular vote. In fact there is no EC wide vote of any kind that determines who the next president is. The presidency rotates every six months among the heads over government of the member states. The rotation is on a schedule that is sometimes manipulated for political advantage. One interesting effect is that small countries control the presidency out of proportion to their population in the EC. I wonder why the EC doesn't elect its president by direct election?