People... TenderDonkey is being sarcastically silly. And will continue to do so as long as you think the comments are serious.
As for the solutions suggested of pocketing pics, CMs trading them with one another, swapping out with a mythical stack, etc... I have one that works even better. Follow the rule, and don't take duplicates.
The Daisy Duck analogy above was excellent, but what really does happen is that people buy the cheap starter sets that contain multiple pins for far less than you can buy singles for. In the past, we've seen the popular themes of Disney babies, chibi versions of the fab five, the collection of stuffed animal prizes from Toy Story Mania... usually, whatever set gives you the most pins for the lowest price.
At rope drop, guests trade these pins right off the bat. If you look, you'll notice that midmorning CM lanyards, especially near the gate, are often made up of close to 50% of these types. If duplicates were allowed, they'd have nothing but these generic starters, and trading with them wouldn't be nearly as much fun.
Now, does Disney mind you trading these starter pins? Heck, no! It gets you hooked! However, to make it fun for everyone, they have a "no duplicates" rule.
Can CMs make exceptions? Sure, on a case by case basis. I've seen CM's give pins to children (one did this for my two year old on our last trip, when he couldn't decide which pin to give away). Are they required to do so, or can they always do so? Of course not. Should you expect them to bend the rules for you, or should you get bent out of shape if they don't? Please.
I sure hope that nobody's child would seriously be crushed by being told "no". I've never seen a CM be ugly about it. My own DS2 was told (gently) that the CM could not take that pin, as they already had the one my child was trying to trade. He simply picked another pin. If a two year old can manage that concept, I fail to see why older folks cannot.
Quit making mountains out of molehills. Quit trying to come up with reasons why the policy sholdn't apply to you, why the policy is bad, ways to circumvent the policy, etc. Understand that it is in place for a very good reason, and adjust your thinking accordingly. Shockingly, you can still have a wonderful time trading pins, even if CMs won't take your duplicates.