I absolutely love exploring all the food and coffee around Melbourne and I can't even remember the last one that didn't take PayPass. Even the market stalls and coffee carts have an MPOS or CBA tablet. Maybe a couple of super hipster places take cash only for the image, but I haven't actually found one yet.
In my experience it's rather the anti-hipster places: cheap Chinese dumplings, Vietnamese noodles etc, typically family run with minimal decor, overhead, wages, cleanliness and tax payments (much easier to underreport cash-only earnings). But often great food if you pick a busy place!
I'd say those businesses will have to evolve or die out. There is a great Japanese place in our town that I stopped frequenting purely because they didn't have an EFTPOS machine, and I often have to cash on me when returning from a customer visit etc. and I wanted a snack to bring home. Since they (finally) installed one after new owners took over, I go back there frequently now.
With PayWave becoming so popular for even $1 transactions at the counter by literally waving your debit card at a machine, I haven't carried significant cash in my wallet for years now.
When they say “cash only” everyone seems to understand it means “we dodge our taxes”. But the food is usually pretty cheap. I’d say they probably won’t evolve unless they start getting prosecuted for tax avoidance...
I totally understand the undercurrent of the 'cash only' operators - but I think that there will always be a portion of your customers who will use cash (travelling tourists etc.) as well as a large chunk who will want to use some form of electronic payment.
Far better for a business IMO to offer both - then they can still pocket most of the cash transactions without declaring, yet still show legitimacy to the ATO by having electronic payment records, which should keep the auditors at bay.
Our town is popular for market and pop up stalls all over the place, and while these used to be cash only for nearly as long as I have lived here, I have been noticing that a lot of them now have portable EFTPOS machines, or smartphones connected to Square or other payment swipers. Especially those that sell clothing or items >$20 because locals just don't seem to carry large notes around any more on a casual basis.
With all due respect, I'd say this is definitely a product of your specific location/life circumstances. I live in one of the biggest cities in North America and "cash only" is not a hurdle for restaurants here.