I always thought about this a lot to. I wondering why they couldn't just swap eyes and both have EMS, but then after looking into it for a bit I understand why. If you go look at one of the pages when Itachi is explaining the EMS to Sasuke during their fight, in one panel there is this monster looking thing that appears behind Itachi, with four eye sockets. Two where the normal placement of eyes are, and two above those. Only the bottom pair had eyes in them, which would represent Itachi's eyes.
The pair above those would be the pair you need to put in to gain EMS, in this case, it would be Sasuke's eyes. Unless all four sockets are filled, the user can't get EMS. That is why you cannot just swap eyes, each brother would still only have two eyes, and not be able to fill in the four sockets.
Edit: Here are the pages. One is of Madara with all four filled, and the other of Itachi.
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Hindsight 20/20 here, I never noticed the Rinnegan above the 4 sharingan on Madara's statue.