pay with credit card, ask for extra cash?

I think you might be confusing credit cards with debit cards.

Merchants are charged a flat processing fee for debit cards and a percentage of the transaction (with a minimum service fee) for credit cards.

The ubiquitous service provided at grocery and convenience stores apply only to debit cards and Discover cards at certain outlets:

https://www.discover.com/credit-cards/member-benefits/cash-over-purcha...

I think you might be confusing credit cards with debit cards.

Merchants are charged a flat processing fee for debit cards and a percentage of the transaction (with a minimum service fee) for credit cards.

Per transaction models exist for credit cards too. I recall there was legislation passed some time ago about this in the EU but I'm not sure what happened to it.

The ubiquitous service provided at grocery and convenience stores apply only to debit cards and Discover cards at certain outlets:

Yes, the comment was made in reference to getting cash at grocery and convenience stores with no fees.

Supermarkets are very cash generative, even in these days of electronic money.

Taking in that cash is a pain for them. Banking is a pain for them. It takes time, it exposes employees to risk, and there's always a delay in the funds clearing in the payer's bank account.

In the UK, a business pays bank charges to pay in cash to a bank. Supermarkets are very happy to let customers have cash back. It saves them costs and time, and is more secure (and may bring customers into the supermarket in the first place - resulting in them buying something).

Well, I guess all we can conclude is that things are different in each country. In the US, allowing cash over for credit cards during purchases would mean forgoing lucrative cash advance (and possibly ATM) fees for the processing companies.

In any case, it would have been most amusing to listen in to the original poster's conversation with the cashier.