America agrees: we need change in higher education. But how do we provide high-quality, low-cost learning to students who want and deserve it? Democratic presidential candidates suggest government-sponsored free college. Bernie Sanders, famed Vermont Senator and high polling presidential candidate, offered the higher education programs in Finland, Denmark, and Norway as promising examples.

But while cost may not be a barrier to student success in these free-college systems, other factors are:

1. Not Everyone Can Go to College

At first glance, Finnish students have enviable higher education opportunities. The Finnish government covers more higher education costs than any other member of the 36-country Organization for Economic Cooperation and Development (OECD), according to the American Enterprise Institute (AEI), and international students rank Finland a top place to study for its high-quality academics, culture, and vibrant student life.

However, few students experience these benefits.

According to the OECD, Finland has one of the most selective higher education systems in the world, with 67 percent of applicants rejected each year—more than double the average OECD rejection rate of 30 percent.

“One reason for the low attainment rate is that Finnish universities have finite resources and considerable autonomy to set admissions standards,” AEI researchers wrote. “Largely lacking the ability to raise revenue from tuition, it makes little financial sense for institutions to admit large numbers of students, and therefore, they are highly selective regarding which students they let in.”

If America embraces free college programs like Finland’s, then like Finland, we must also face the possibility of trading an expensive higher education system available for all, for a tuition-free higher education system available to only a few.

2. Disadvantaged Students Left Out

While politicians like Elizabeth Warren suggest that free college will put disadvantaged students on a path to success, Nordic higher education models suggest it’s not that easy. In Norway for example, students need only apply and be accepted to a higher education program and the government will cover the cost of tuition. But the data suggests that students from less-educated families aren’t making the transition.

According to the OECD, only 25 percent of 25-to-64-year-olds whose parents have not graduated from high school, have received degrees. For 18-24-year-olds whose parents have not completed college, only 39 percent earn degrees, even though they make up 53 percent of their age group overall.

These numbers don’t necessarily mean that young Norwegians from less-educated families are worse off than their peers.

“A bachelor’s degree in the U.S. has been seen as one serious option for getting into the middle class, whereas in Norway everything is a ticket into the middle class, because everyone is in the middle class,” Curt Rice, President of Oslo and Akershus University College, told The Hechinger Report. “It’s now less clear that it really is a ticket into the middle class in the U.S.”

But if America’s goal in adopting a free-college system is to educate those from disadvantaged backgrounds, the Nordic model suggests that free college may leave us disappointed.

3. Fewer Students Graduate

Like Finland and Norway, Denmark also covers tuition for higher education. Better yet, Danish students receive a monthly grant to cover housing and living expenses.

But many students still aren’t graduating.

Although 81 percent of eligible students in Denmark enroll in higher education programs according to the World Bank, only 40 percent of 25-64-year-olds have earned a degree, according to the OECD. Norway has similar results. There, 82 percent of eligible students enroll in higher education, but only 43 percent of 25-64-year-olds have earned a degree.

The United States fares better on both counts. Although American government covers significantly less of the cost of higher education (35 percent as opposed to 96 percent in Norway and 92 percent in Denmark), 89 percent of eligible students in America enroll in higher education, and 47 percent of students age 25-64 have earned a college degree.

These outcomes make sense. Why would a student graduate, join the workforce, and pay for their own living costs when they could stay in school and explore career opportunities on the government’s dime?

“With education being free, the Danish word ‘evighedsstuderende’ has risen,” Daniel Borup Jakobsen, a 24-year-old recent graduate and vice president at the software company Plecto, told Business Insider. “It refers to a person who never finishes his studies but continuously keeps changing study program year after year.”

While we certainly should revolutionize the way we think about college, expectations of free college don’t match reality. If we want higher education to allow access for many, put the disadvantaged on a path to success, and develop students who are eager to contribute to society, then Nordic examples suggest free college may not be the way to go.

Fortunately, good old-fashioned American innovation offers a way forward. Apprenticeship programs provide access to jobs without incurring the cost of traditional college and for the few jobs that require higher education, income-share agreements foster investment in promising graduates. As these programs continue to grow, students will continue to face new opportunities to pursue the careers and education they aspire to without the disadvantages of the Nordic “free” college model.