As others have said, we're both wrong (it's area attacks, not close attacks, that are the other case) - but that's peripheral, really.
It's peripheral to your point, but it's still a reasonable demonstration of how "move without shift, plus ranged and area attacks" is a harder rule to remember than it would seem.
But all of that ignores the real complexity of the system: shifting. The best reason to get rid of OAs is to get rid of shifts (and five-foot-adjusts).
In 3.x, we had a "five foot adjust", which was a special weird little rule. In 4e, they generalized non-provoking movement into a "shift." That's a fine rule for tactical folks, and at least half the players I know never had trouble remembering it. But it's an extra thing to explain and it generated another abstract rule: "move actions" to handle your various choices of how to move.
Move actions are organized and neatly understandable, but they are abstract and require explanation. I can remember the expressions on the faces of players when I explain that you get a standard action, a move action and a minor action. Nearly every person understands it, but new players need to concentrate on it. When it gets to their turn they think "I have three types of actions, what do I do with them?"
That's fine for a tactical skirmish game, but lousy for a role-playing game. In a RPG, players should be thinking "what do I want to do?" not "how do I spend the action currency I've been allocated?" If focuses new players on rules abstractions, not the in-game fiction.
The other reason to can OAs, is that they force players who haven't internalized the OA rules to think carefully when moving. The exact details of their movement is rarely critical to the game, and careful thought dedicated to usually-irrelevant detail slows down combat. It's far better for players to focus on their actions.
-KS