My grandma had a store for 40 years in Italy and she was a cash-only person, too. She had a bank account, a card, checks... but that's as far as she went (checks). She never used the card and when she tried to use it, she didn't know how to navigate the ATM screen and the machine 'ate' the card. I was 10 years old back then, so I was useless in front of an ATM because I didn't know what the various options prompted meant, I just knew how to push the buttons - it never occurred to her that maybe she had to push the buttons on the side of the screen to select an option - she stopped at the keypad.
When I was a teenager I had my bank account and my card and tried to convince her to use it. I was using mostly because it was cool (none had a card they could use by themselves, without parental supervision) and the 'cool' argument was never convincing enough for her.
In her eyes, the money was not safer in the bank, it was just harder to access. Suppose you needed the money, but pushed the wrong buttons at the ATM... you would have ended up with no money and no card, so more troubles than what it was worth.
Instead, she always kept a wad of cash at home (about €5000 in current money), and even when shopping in bulk for her store, she always paid cash. She retired in '99 or around that time, so this was 20 years ago, but I doubt much has changed in Argentina, where many people are wary of banks here and have tried to avoid them as much as possible.
If people haven't been used to banks / bank services for most of their adult life, they will hardly join the banked squad when they are older.
I have had the opposite issue when we moved to Argentina. I always had very little cash in my wallet when I was living in Italy. I could pay by card about everywhere. The only cash I needed was for drinks and coffee, because at that time no shop accepted card payment for smaller amounts.
When we moved to Argentina I felt very controlled because I needed cash for everything, and my husband kept the accounting. I still cannot go on a shopping spree unless we plan for it in advance, and then I feel bounded to buy because maybe we have changed money on purpose, and the longer the money sits in our hands the less it's worth. Sometimes I have to ponder whether to buy something non essential or keep the money for the food because it's Friday and that money has to last until Monday. Or maybe because I would need only $2000 more, but the minimum amount you can exchange is a 100 USD bill which is about $8000 nowadays. What to do with the remaining $6000?
Overall, it's a continuous calculation and pondering, not to mention the discomfort of having to look for a place to exchange and go around with a lot of pesos, becoming a potential target. Money management is a worry I didn't have in Europe.