I think this example clearly illustrates the major flaw in their contest and one which could be remedied at minimal time expense to EA. Send a QUICK email reply to each entrant thanking them for their entry. And NO, don't do it with some script, but manually type a short message.
For Spada, Chrissay, and others that might see this thread, try putting just the littlest personal touch in your customer service now and then and see how far it goes. I'm sure this contest didn't garner 10,000 entries. A sincere thank you for your entry would have prevented this.