An area depopulated by the sword then simply left fallow? or too much for any surviving locals to be able to clean up after?
Two things -- these are the remains found so far, and two, the rest of the population was probably carted off into slavery, not necessarily all that far. Ordinarily there would be fill-behind from neighboring areas, which is what happened a bit later. Looks like Copenhagen was a Roman territory, and used to control seagoing traffic and trade between the Baltic and the North Sea.
Several iron smelting furnaces, blacksmith forceps, hand- made ceramics and plenty of iron slag were uncovered at the site.
The Vikings smelted iron to make nails to hold their boats/ships together.