When you're in a society where it financially doesn't matter which career path you pick, you're completely free to pursue a career that will make you happy. I'm not forced to "gamble" on college. I'm free to choose to go to college, if that will make me happy. The only limitations are my abilities, and the quotas on certain educations, because we really don't need that many lawyers or people with degrees in "French 19th century painters".
You equating success with money, and that's not really the case when you're ensured, well almost, that what ever you do, you will pay well enough.
Of cause there are poor people in Denmark, of cause there are people who absolutely hate their job, and there a tons of people that would rather have a well paying miserable job, than a fun low paying job. Denmark is not a countries filled with hippies, where everything is perfect and everyone gets their fair share. There's people who have be extremely careful about how they spend their money, if they don't want to live of pasta the last week of every month. BUT their children, if they have the abilities and the desire, have the option, for free (plus 800USD per month to help pay for food, rent and books), to go to college... or become a well paid carpenter.
In the US going to college is a lot like going all in on a hand of poker. It might turn out really well (good job, pay of debt quick), really poorly (no job, crushing debt, find work that doesn't require and isn't related to your degree) or somewhere in the middle. The better you are at what you do the more likely it is to turn out well. If you're not financially prepared to lose then losing is going to suck. When going college can be the difference between being running a really good HVAC business and sitting in an air conditioned office designing those components, and there's a huge quality of life difference between the two, going all in seems more worth the risk.