I enjoy how you think.

The difficulty I have in correcting you, which is only trying to pursuade you to see it my way is that you might not need any correcting. Furthermore if I correct you then I might not learn as much from your posts as I could. I think that I can work from these two sentences:

As I see it, there are always two 'redeeming transactions' in this practical scenario. The deposit and the withdrawal.
The Demand works immediately on the backside of a paycheck if you are cashing it; which is a simultaneous deposit and withdrawal if you will. Deposits are not taxable as they are credit on account. So if you deposit your paycheck then you only sign your Demand to be consistent with doctrine. That means that you will be withdrawing funds later on a different paycheck, written by you to yourself often called a withdrawal slip. Or you can just write a check to CASH. The custom of changing the Signature Card is for electronic deposit from your employer and when you pull paperless withdrawals like with an ATM, or maybe even when you are in a hurry, forgot your stamp etc.

Equivalently you are telling your bank by Notice and/or Demand that all deposits are special. Not general or regular deposits.