No tuition fees and generous grants give young Danes an opportunity that would make most green with envy -- a university education without a massive debt yoke.
But many, in both industry and politics, feel it's become a free lunch that's giving indigestion to Scandinavia's already weakest economy.
Too many pursue "fulfilment" and too few the science and engineering degrees needed in well-paid growth sectors critical for the nation's future, they say.
Typical is 23-year-old Ali Badreldin, who is enrolled at the Royal Danish Academy of Music to become a saxophone player. "Music was always part of my life growing up so it was a natural choice," he said.
His courses are free and he gets a monthly stipend of 5,839 DKK (782 euros, $1,074) in a system where class sizes are rarely limited.
The result has Denmark spending more proportionally on education than any other country in the OECD club of 34 advanced nations.
Yet biotech firms like Novozymes say they cannot find enough engineers.
Engineering opportunities have soared in recent years in Denmark, but its youth have shunned the sector, with only one-third the OECD average contemplating an engineering career amid top-heavy enrolment in arts and humanities programmes.
- 'Education as investment' -
Novozymes, along with toymaker Lego and healthcare products manufacturer Coloplast, felt it was time to hit back with a major advertising campaign to woo students.
"Many young people want a meaningful job, and I think we need to become better at explaining the difference engineers are making," said Novozymes human resources director Michael Almer.
Conservative critics, meanwhile, say all is too easy in a cradle-to-grave welfare state where youth unemployment, at 14 percent, is noticeably lower than the EU average of 22.8 percent, according to Eurostat.
They point to "Lazy Robert", or Robert Nielsen, an erstwhile student of social sciences, philosophy and Chinese, now 45, who shot to notoriety after proudly stating on TV that he prefers living off social benefits than taking a job he didn't find "meaningful".
For Mads Lundby Hansen, an economist at free market-leaning think tank CEPOS, students should pay at least part of their studies .
"My advice is to introduce a limited tuition fee because it would make young people consider what kind of job and salary they will get. You begin to think about education more like an investment," he told AFP.
- Political hot potato -
Countries like Britain have used the financial crisis to justify tuition fee hikes, but talk of even nominal fees has proven a political hot potato in Denmark.
Last year, Venstre, the largest opposition party, was roundly accused by the ruling Social Democrats of "gambling with the welfare and equality ... we have built up over generations" when they suggested a school fee proposal, which was promptly killed.
As the debate heats up, Danish universities have pledged to reduce admission to fields where unemployment among graduates is high.
Not all agree. "The problem is not as serious as some people would have it," said Palle Rasmussen, a professor of education and learning research at Aalborg University.
"If there are some courses that don't lead to jobs, students will eventually avoid them," he said, arguing that unemployment benefits are no longer as cushy as they once were in Denmark.
Overall, only 48 percent of Danish graduates end up working in the private sector, compared with an EU average of 60 percent.
Some say only major change, both fiscal and ideological, will encourage more students towards well-paid growth sectors.
With one of the highest tax rates in the world -- at 56 percent for top earners -- big salaries mean mostly bigger taxes to sustain the welfare state. Many young Danes just don't see the point of putting in years of effort into studying for a bigger salary eaten up by taxes.  
Others, like music student Ali, remain convinced that all will work out if they follow their dream.
"If you study something you are passionate about you have a greater chance of making a living from it later," he said.