That's pretty crazy considering Denmark is touted as a socialist utopia where the taxes are high but it's worth it because the government supposedly takes care of everything for you. I'd expect them to have figured out the doctors' shortage but this problem seems endemic in every country.
In EU, there is a severe shortage of MDs. Part of the problem is that the number of students is not sufficient to satisfy MD demand. In some countries, this is a deliberate policy imposed by MD lobbies, who act like a cartel. In other countries, the job is simply not attractive due to relatively low salaries and high workload. So students choose other degrees, or they immigrate after graduation. Furthermore, an aged population and lack of adequate policy planning does not help.
This is the thing, even in the US with salaries 2/3/4x those in Europe, people in much of the country can get appointments for the better part of a year.
It's a matter of "current patients have filled the schedule indefinitely."