Counterpoint, if the customer places the money on the counter for payment, how is there any issue if the cashier returns change by placing it on the counter?
What is considered polite may differ by region and culture. (I’m not claiming you specifically would be upset at this, it’s just relevant to the meme.)
Either put both the coins and bills in your pocket together and sort it out later, or don’t pick your items up off the counter until you sort out your change.
Because even if they gave your paper bills back separate from the coins, if your other hand is so occupied with the items you purchased, how were you going to get the bills in your wallet anyway?