Anecdotally I've noticed that among the coworkers I've had from other countries, the ones who manage to learn danish and stay, have generally been in areas with lower density of foreign workers.

My theory is that in areas with lower densities of foreign nationals, you'd benefit more socially form learning the local language.

This makes sense. By default, foreigners stick with their fellow countrymen pretty much everywhere. Not having them around gives foreigners a reason to socialise outside their bubble. I believe this is the reason why Denmark has the so called guetto laws.