I need to buy 10,000 plastic ID badge holders (with an attached string
so you can wear it around the neck.)  I'm looking for the cheapest
possible ones, I don't need anything high-quality, or with any frills.
 The cheapest price I've been able to find for 10,000 is 16 cents
apiece, however, I can only afford to spend (at most) 6 cents apiece. 
I considered buying plastic baseball card sleeves instead (which I've
found selling for just half a cent each) but the labor that would be
involved in manually attaching 10,000 strings would just be too much. 
I still can't understand why simply adding a string causes the ID
badge holders I've found to cost 32x as much as a baseball card
sleeve, though!  Can someone help me?

Because you are buying in volume, you are in a position to purchase
factory direct.  The prices you were quoted were probably from a
distributor after their markup.

You will be surprised to find how cheaply you can find products
factory direct from overseas factories.  Considering the exchange
rates and standard of living, Do not be surprised to hear that
Americans pay as much as 4,000% markup at retail, over the original
factory prices on some items.

Here is a link to a supplier for a no-frills plastic badge holder that
you are looking for:

http://sail.chinasuppliers.alibaba.com

This product, as displayed, does not include the lanyard that you are
looking for, however, this company also manufactures lanyards, and you
should be able to negotiate a deal for id badges with lanyards, maybe
even for less than you expected.

After arranging payment to the factory, using FedEx or UPS, you can
have your products in a matter of days.

www.alibaba.com is an international buying and selling marketplace. 
You can also use the website to search for other suppliers of the same
sort of product you are looking for.

http://www.alibaba.com/bin/sample/search?s=0&n=10&key=id+holder&country=&ShowCategoryNums=10&ShowCategoryStart=0

It turns out that the link I posted earlier was for the company
homepage - this is the link for the specific item you are looking for.

http://sail.en.alibaba.com/offerdetail/50398221/Sell_Clear_PVC_Wallet.html