The system as it is now in Denmark is unsustainable. Most people don't work. The government is running a deficit. And the outlook is very low growth and Denmark is going to be the poorest northern European country.
It used to be in the top 5 of the richest countries in the world.
Besides the government deficit and debt, the population also has high private debt. http://online.wsj.com/article/SB1000142405270230444460457733...
One of the good things in Denmark that you don't have in most southern European countries is that you can fire people easily.
BTW Denmark has had the school voucher system for decades.
edit: According to this site Denmark is more economically free than the US: http://www.heritage.org/index/