I am Italian, from Rome, but lived everywhere in Italy, from North to South, sometimes for long periods, sometimes for as long as a week.
What you noticed is true, but it's simply a reflection of past history, where Italy was a group of villages/towns independent (and often at war) with each other.
Italians are often chauvinists and defend local over global, no matter the evidence.
But, truth is there are more Sicilians in Lombardy than in Sicily, Rome is the largest city of Abruzzo (there are more people from Abruzzi in Rome than in L'Aquila, the capital of the region ) so what happens is that they recreate their local culture where they go and slowly with times the traditions become a mix that incorporate both cultures.
For example in Milan, where I lived for the past 8 years, it's easier to eat Sicilian, Pugliese or Chinese than a typical Milanese cuisine, but it's almost impossible to find a good Roman restaurant.
On the other hand, locally, the separation is usually stronger, it's true that culturally a random village from Trentino is different from a random village in Sicily (and there are historical reasons, Trentino is kinda an outlier in Italy, it's been Italian for a relatively short period) but it's also true that a random village near Palermo is different from a random village near Siracusa.
My parents come from a small town 100kms South of Rome and in that same town the eastern and western part speak two different variations of the same dialect and also the typical dishes are different. they are only fee kms apart.
My point is that in Denmark homogeneous population is only part of the reason, the most important one is being historically a united country under the same traditions that are valid throughout their territory and keep them together. Also a small population makes it easier, Denmark has the same population of an Italian region like Lazio, where, more or less, the culture is uniformally the same and the roman culture is more prominent than the rest of the country.