You could also just write an arbitrary date and the name of the most convenient shop when it fails, so I really don't see what good that does, it's very far from a receipt.
At the very least, it gives you an idea which receipt to look for in your box of receipts/warranties.
And no, I am not happy about having to think about storing receipts for mundane things like light bulbs either, but it is the only thing that calms down my nerves when yet another bulb with 5 year warranty fails in a year.
If you run a store, and a customer comes in and says "I bought this item on $x date; I don't have the receipt but this is how I know", you have two choices:
a) you can choose not to trust them
b) you can choose to trust them
For a $3 item, most retailers would pick #b every time.
