Anyone finesse customers into not taking cash?

I work as an ASM, and honestly, taking cash has to be a big waste of time. 7 minutes to the bank in the opposite damn location or where my house is. What? Also not to mention all the steps, and counting 50 times to just double verify I don’t put the wrong crap in the bag like the wrong amount. This especially applies because if our drawer is short too much I don’t want to get fired like the company would do if that were to happen but I don’t know. Anyone else have this? It’s just a big time grab, and always get help up way past closing. What do I do?

“Sorry, drawer doesn’t want to open”

Sometimes it works well but sometimes people carry their whole bank account in their wallet and truly don’t care what it costs somebody else to go. Anyone have any tricks or experiences where you just don’t take cash without intentionally refusing service? Is that even possible to do? Just curious doesn’t mean I’ll do it but seeing if anyone can relate to this.