I think something more interesting might be like a voronoi diagram of all cities such that the city is in like the top 5 within a 1000 miles radius or something (or just that but without the voronoi part). This should preserve the fact that only the largest cities in some area are present, but eliminate the arbitrariness of the boundaries. I think you would want to compute this with a sweep line algorithm.
A map projection that preserves area would be better, otherwise there's an excessive number of cities in the far northern hemisphere, and a lack of detail in the tropics.
Denmark has a funnier case. There are 6 cities/town within the Kingdom of Denmark with 0 of them in Denmark. (5 in Greenland and 1 in The Faeroe Islands; Iceland belonging to the Kingdom until 1944 has 2)
Mercator can be a very useful map. Angles are not distorted. It's also very good at low distortion at small scales. As you zoom in on a point, the area distortion diminishes. Once your area of interest is around 300km wide, the area distortion is only about one part in one thousand. It converges very quickly on a "true" representation of the earth.
Mercator's ubiquity isn't due to people who "aren't into maps" but rather because its strengths are really powerful in many use cases. Imagine the confusing situation if, in your favorite Maps app, North weren't always directly up, intersections met at wrong angles, and square buildings didn't always look square.
Those strengths being in navigation: straight lines in Mercator maps correspond to a constant bearing in the real world, which is really handy when your ship needs to cross thousands of kilometers of ocean.
