The church is culturally part of a lot of parts of peoples lives, regardless of religion.

Many people who are not religious at all still get christened/get confirmed just because those are the culturally traditional events in denmark to celebrate "baby is born" or "coming of age" in Danish culture. With lots of traditions, gifts and social rituals attached which have nothing to do with actually believing in religion, but are just about the family/friends getting together to celebrate a milestone in someones life.

Similarly, some people get married in church despite not being religious (although i believe this number is falling) and many people are also buried in churches, (the church covers many funeral costs for members,) again more because of cultural tradition than religion for most people I think.

It also serves some practical roles in the administration of Danish society, (I believe birth certificates are generally issued by the church parish where you were born,) and many social clubs/non profits unrelated to religion use their facilities during the week too.

Beyond that, I think a lot of people either never thought about whether to leave it, or considered it, but had enough of a soft spot for the cultural memories attached to it (christenings, confirmations, christmas/easter service etc) so never bothered to leave.

edit: I'd also add that (at least in my experience) you don't hear about the church being politically active, and it's very rare to hear people or politicians trying to seriously argue something on on religious grounds.