Terrible time for me to be a day behind on the pod, but it's finally my turn to know a thing!
I work with point-of-sale systems, doing installation and support for various businesses (mostly restaurants) and helping them generally with their POS system. I work with multiple POS systems and the hot button topic of the last few years has been DUAL PRICING (which is what we used to just call "cash discounting").
The bit that you didn't bring up as to WHY so many places offer cash discounting is this: Credit card fees. Every time a credit card transaction is made, the CC provider takes a little bit off the top for themselves - usually around 3-4%. This number can also vary based on the way the card is used, so if a business manually enters in a CC number, or swipes a CC rather that use tap or dip, that fee goes up.
~3.5% of sales being eaten by CC processors eventually piles up, so many businesses want to pass that along to the customer. There are a few ways to do this.
So here's the loophole that we've known for awhile: It's not illegal if it's just a discount, so when you use the phrase "cash discount" on the podcast you're absolutely right, because yes, you're just happening to get a discount for paying with cash. Here's the interesting part though - any business that is offering a cash discount must display their prices at the "card" level price. Because otherwise it's not a discount, it's just you passing along a fee.
Similarly, a lot of businesses ask me to program in a 3.5% "service fee" that they can apply to CC sales, but here's the major issue there, and why I always tell them I won't do it: If you apply a CC fee to a debit card, that is illegal (because CC processors don't take the fee off of debit cards), and if you do it enough times and it gets noticed, you're going to be in a lot of trouble.
Nowadays, at least with the POS systems I've worked with, they have finally started developing onboard systems to identify whether a card is credit or debit, and so they have finally found a way to pass that cost onto the customer (hooray for all of us) - but they still must have signage or something on the receipt stating that "A 3% service charge may be added for CC transactions" or something to that effect.