That bank interaction is obviously too cumbersome to withdraw $80+ every week to pay cash for taxis. If all taxis refused to take credit card then yes, I'd have to use the ATM on a regular basis.
You're right that cashless was only possible recently. Even though credit-cards had been around for 50+ years, most people couldn't go 100% cashless because many places like McDonald's fast food only took cash. Those restaurants avoided credit transactions because having customers wait for the charge receipt and then sign their name clogged up the queue with impatient people. However, a recent revolution in payment processing allowed "no signature" transactions for small amounts under a threshold (say $20). The "no signature" includes not having to electronically sign the touch pad -- it isn't just avoiding paper and pen. With that change, McDonald's started accepting credit cards in 2002. People also might notice that when they pay by credit card at Starbucks, they don't have to sign anything. Credit transactions are now so fast, the situation is reversed: cashiers take longer to count out exact change for cash transactions than let customers pay by credit card!
The "no sign" revolution helped make lots of the "cash only" places disappear so now it's very easy to be credit-card only.
I'm curious how this is possible or if you're exaggerating. I live in London, so a pretty well connected city, and although I can use card/contactless almost everywhere I still need cash about once a week as some small places won't accept card. 10 years ago I'm sure cash was much more necessary.