Cash from some banks may trade at a discount to that from others.
This is also exactly what you mentioned here:
One distinction I will stress here is that it will rarely be precisely 1:1. There should NOT be an expectation that an Ecash will ever redeem the exact amount of Bitcoin because of the fees involved. You can never go directly to the source to get the same amount of Bitcoin as you entered. The same concept can be applied to other layers, such as Lightning. A sat on LN is valued differently than a sat on-chain. This is important to understand the actual cost of Bitcoin ownership, the cost to control and manage capital in a blockchain, and how market rates will be determined.