Lots of places have been cashless for ages. You can't use cash (to buy tickets for onward transport) at many airports. (The first time I encountered it was at Charleroi Airport in Belgium several years ago). You can't use cash on buses in London. There are quite a few restaurants and bars that no longer accept cash. (The first one I saw was in London, at least five years ago). The majority of people who order food in McDonald's now seem to use the self-service ordering points, where only cards can be used. The Asda filling station in Bury St Edmunds is 'pay at pump' only, with no kiosk, so that only card payments can be made.
I do my best to avoid all businesses that don't take cards, preferring not to patronise dinosaurs. The only times I use cash are in the launderette, at the local burger van (although most of the other burger vans around here take cards), at the barber's and when using on of the very few car parks where card payments aren't yet accepted. I withdrew cash from an ATM earlier today (because I was going to pick up my washing from the launderette) and realised that several months have passed since I last used an ATM.
Many of the problems which seemed to prevent barriers to moving to a wholly cashless society (such as how to give kids their pocket money) now seem to be getting ironed out, so hopefully cash will be a thing of the past within not more than a year or two.