First, "indebt their youth basically for life" is just false. Just 1/3 of people 18-29 in the US have student debt at all: https://www.pewresearch.org/fact-tank/2019/08/13/facts-about.... 40% of college seniors take out no loans at all.
Out of people who do have debt, the median student debt for someone with a bachelors degree is $25,000. That's less than the average U.S. new car loan. Over a career, a typical college graduate will pay much more in extra taxes in one of those countries with "free public education" than the $25,000 median student debt for college.
Second, the United States has "free public education." The question is do we need to extend that to tertiary education. We sent a man to the moon back when just 5% of adults had a college degree. It's not clear that sending vastly more people to college is actually going to add value.