Thats a nice saying and I hate to ruin it but believe me most people in Denmark knows that the tax on fatty foods is just an excuse to bring in more money to the government.
I mean are you really going to buy less meat because it went up 5%?
You might not, and I might not, but some people will. Like a lot of things in modern society it's all about the margins. The effects of such a small increase aren't flashy or obvious, but they're still real.
A vice tax on fatty foods makes no sense if (1) you are trying to improve the health of the populace, and (2) you know about the health benefits of ketogenic diets[1]. If those are Denmark's goals, then they should instead be taxing sugary foods. Otherwise, I am forced to conclude that Denmark is either (a) dumb, or (b) purposefully decreasing their citizens' health.