Depends on the situation. I know that if you were applying for a mortgage and we needed rental verification, it would be tough to use reciepts. The reason being, anyone can fake a reciept, it's a lot harder to fake a cancelled check. Of course, you sound like someone with more than sufficient credit to not even need any conclusive proof of rent, but that's another story.
The receipt provides the number of the missing money order. If it doesn’t show up to the seller, the product doesn’t get shipped, I check with the bank to see if it was returned and I’m issued another since it was lost. I don’t know how much easier that is.
I can’t see the advantage of someone trying to steal a filled in money order especially after I scripple all the information needed for the transaction.