I am not sure what you mean. Danish government is cutting down primarily in the humanistic fields around 4000 chairs all in all. A lot of people who live in Copenhagen go to "University of Southern Denmark" it's not so important where it happens.
Denmark have way too many people in the humanistic field and they are rightfully cutting that down.
Also keep in mind. Education is 100% free plus you get subsidized when you take education.
I just think theirs a higher chance that you'll stay in the area where you took your education. so in that regard some areas might go short on workforce in a few years.
Apart from that you are all right. I get "paid" for studying, which of course comes at the cost of my earning being cut in half or well less for the rest of my life, do I decide to work in Denmark.
I think and have thought for a long time that you should lend the money instead, so that you won't have any people just studying to "leech". But maybe that's a discussing for elsewhere.
You are right that Denmark is a small country, I've been to USA too, and I talked to a lot of people working in cities 2-3 hours drive away. So by that yes.
However, and I might be somewhat wrong, but I've seen more people beginning to crowd around either Odense, Aarhus or Aalborg the last few years. This is however my own observation from students who finished their education that I've run into.
Denmark have way too many people in the humanistic field and they are rightfully cutting that down.
Also keep in mind. Education is 100% free plus you get subsidized when you take education.