I don't get where the exploits come into it?
You spend 5 eggs to gain one egg? Your basically burning 4 eggs.

How can 1 egg be used to get the achievement within an hour? I don't think having +1 egg for every 5 immediately means things are particularly easy mode all of a sudden?(realistically it's +1 opening of an egg for -4 eggs)

Have i read it wrong, does this item have more than one charge as well as a 1 hour cooldown? The only exploit i can see is if a main character found he prematurely got all of the achievement items via drops from finding the eggs himself in the last 10 or so eggs he picked up when farming for the full potential 475 or so eggs.
Then due to the unexpected eggs the main has left over and nothing to buy all of a sudden he buys up all the ones he can lay manually and dumps them down in some corner where an alt could pick it up.

1hr cooldown fixes that scenario and tbh it's the only problem that i can see that could come of removing the cooldown. It's essentially there to stop people who finish the looting achievements unexpectedly from trading in there remaining eggs and trying to use them to give others an easy ride(as if it were hard anyway) otherwise it's a waste of chocolate.