Cash is an anonymous payment system which cannot be traced and is widely accepted. It's something that would be impossible to bootstrap today if it didn't already exist. Hence, it's crucial to keep it alive.
I just wanted to point out the possibility of tracking serial numbers on bills. Obviously it's not going to be as reliable, at least not now, but it could be made more so; for instance, if there was a sudden movement to use more cash for privacy. Of course, that seems unlikely; most people like the convenience of plastic/digital payments, and there's a lot of market pressure pushing people toward those payment methods, so deploying the infrastructure for more reliable cash tracking probably isn't worth a whole lot. But I haven't exactly run the numbers, and there are other possible incentives, so who knows..
Ironically I started to appreciate it, after I received a fake bill from a different store.
Not really; bills are individually identifiable and can be tracked by either party to the transaction, and even if the payment medium isn't tracked, the transaction can even tracked by other means (e.g., cameras + facial recognition.)
It's only really untraceable if you assure privacy of the location of the transaction, and neither party to the transaction chooses to track it, and even then if the next party out on either side is tracking, a lot can be revealed.