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In Germany Aldi has such a market power that even for the few name-brand item they stock[1] they can demand different packaging from the manufactures. That includes not only barcodes but sometimes even more explicit ingredient lists.

[1]: Recently they started to stock more name-brand items due to a strategy shift. The other chains are not very amused.

They have enough buying power - they could probably mandate it

Costco certainly asks for custom packaging. No other retailer is going to put an SD card or bottle of vitamins in a 2 sqft blister pack.

They have their own Item Number system. Even general-retailer items sold elsewhere often have the (Costco) Item Number on their packaging.

Costco could just print their own and add it to the packaging.

I'm not sure that the time needed to affix the label to every product is less than the saved time due to faster scanning.