In my country I can withdraw cash from the machine as I pay for shopping at the supermarket. And I'm not saying I withdraw cash then pay. I pay with the card AND the cash I withdrew comes out after the transaction is complete.

I haven't been to a bank for getting cash in 10 years. And as you say, ATMs are where you get cash.

We can do that here in the Mid-South, too. Got a story you might like. The customer, service desk which allows some cash back for free was packed. So, I had to go to register with something to buy. I tried to minimize the cost overall for a $500 withdraw at a company with $100 max per transaction. I hit their self checkout. I did five orders on the machine each with a single grape. Each order was one cent plus $100 cash back. Total transaction cost was five cents.

Self-checkout person was going "what the hell?" on that one. I also heard her talking to others about being hungry from break being delayed. I gave her the grapes after explaining what I was doing. She was happy, too. Probably did it herself at some point haha. Cashiers trip out to this day if I tell them about that whenever someone is buying a candy bar or something to get cash back. Occasionally, person in line leaves to get a grape. Just one. :)

Hence, if your wallet is stolen, you go to the bank, not the ATM.

But I actually assumed just the cash was gone. Either bank or ATM works fine in that situation.