There's been talk of shops actually abolishing the use of cash. So far without success, but most transactions still happen through a nationalised credit card system.

Cash use is about on par with most other countries. Credit cards & mobile solutions are slowly rising, but cash is still widely spread and necessary in some cases (like paying for public transport in certain cities, etc.).

Not in my experience. I almost never carry cash when in Denmark. In Copenhagen at least, it feels like the only place where cash is required is the pølsevogn (hotdog stands).

In Spain where I am based now, and in New York where I spend a lot of my time as well, I always have a bit of cash on me because small purchases have to be made with cash.

Definitely not. Considering myself quite the traveler, I'd say Denmark is the country I've visited that by far has the best support for credit cards, especially Copenhagen.

Just spent 6 months in the US and we in Denmark are way ahead in regards to a "cashless system".