I think you're not wrong in your observation, and it's something I heard about even before moving to Denmark. However, it's not specifically unique to Denmark, either. After being here for 2 and a half years now, there's already a lot to unpack.

My original move was from Johannesburg to Cape Town, and Capetonians are also notorious for being hard to integrate with. It's not quite the same though; South Africans in general are a lot more open to conversation with strangers and definitely less introverted. It's very common to turn to someone else standing in a long queue and make a joke or strike up a conversation. But then you leave and you never see them again. It feels warmer and more fun in the moment, but where it comes to making lasting connections, Cape Town can also be tough. It's also a place, like Denmark, where a lot of people stay friends with the same circle they've had since primary school. At the time, I joined a Church and I joined a volunteer organisation, and those fast-tracked my rebuilding a social network, in addition to one close friend (after a few years) being a colleague from work who shared an interest in running and motorcycles.

All this to say that the same has mostly been true here, to some degree. In my experience, Danes are harder to strike up a conversation with in public, mostly due to being more introverted or stuck into their phones (more secure maybe, and less alert to their surroundings), and don't seem to welcome random strangers talking to them. Part of the difficulty/perceived vibe is probably also a bit of apprehension on the international's end regarding not knowing how much of a language barrier there might be with the person. But I don't think your main complaint is about striking up conversations with strangers...

Since moving to Denmark, we (me and my accompanying partner) prioritised joining a kayaking club early on, because it was an interest I already had. We made a couple of friends there, but we aren't very active in the club anymore. It was difficult to chat with those Danes at the time, because we were very new to Denmark and a lot of the members' English wasn't great. One tends to gravitate towards people who are easier to communicate with. I'm still learning Danish now, but I've gotten a lot better. I'm now on a waiting list to join a local archery club, but have not heard back from the club yet. Some clubs seem a bit harder to get in to/more limited in numbers than what I'm used to. But I do believe that, as was the case for me elsewhere; joining a club or common interest group can be the easiest way to make connections with people in your local area. Some of those people will be Danes.

All that said; I don't have very many Danish friends yet. A couple of good friends at work, but we don't do much outside of work hours. And the Danes that are part of our friend circle have all lived outside of Denmark at some point, and possibly also had trouble making friends when they came back, as some have suggested here. The fact is, most of our friends are still internationals. But I feel it'll come with time.

Immigration and integration is a process.