There isn't a gun culture* (just picking one aspect) at all in Denmark, there is a rich culture in the US to the point that people think you are changing the identity of the country if you reform gun law. Stating that a progressive state that never had such problems can solve them has no meaning.
* guns would be the leading cause of homicide in the US.
Like a trigger is a leading mechanism, but it's the combustion that fires the bullet?
The gun/trigger/bullet/gunpowder/whatever is a mechanism of the murder, not the cause. (I'm not a rabid "gun nut" [nor even a gun owner], but blaming guns as the cause is just as fundamentally misplaced as blaming a baseball bat, knife, or rope, IMO.)
Removal of guns from a society lowers total murders, it doesn't just move those murders to some other weapon/cause.
Look at Australia's crime statistics, or Canada, or Britain before and after serious gun control. They all show this to be true.