If they don't now, they will in a few years. We had the same evolution here in Belgium & the Netherlands, late 1990's or early 2000's recruiters wouldn't ask overly let alone require it. Nowadays they try hard to get you to disclose. I think one of the reasons is what is cited above, for the statistics for internal use. In time they will get more sophisticated and they'll start asking.
Aside, isn't there a website in Denmark where you can look up people's salaries? Or is that in Sweden?
I still haven't been aggressively asked by employers what I make now, but I have been asked aggressively what I wish for (as in, you tell us first and we'll say yes/no/maybe).
Even Jack Chapman from "How to make $1000 a Minute" (highly recommended) is not sure any longer.
I currently tend towards telling what I want (because I want above average), it might be better to wait if you consider yourself sub-average.