In Germany, tuition is almost non-existent (usually some fees of maybe 150€/semester, although a few years back there was a phase of actual student fees of - still laughable - 500€/semester), and if your parents don't make much money, or if you have many siblings, you can even get a half-credit/half-scholarship from the government (AFAIK even without interest, called "Bafög"), so especially for poor kids it's as easy as nowhere else in the world to go study. In smaller towns you can also get a student dorm room for under 200€, and overall living (esp. groceries) in Germany is quite cheap.
Yet Germany has a very low number of working-class students, for whatever reasons. Usually I think it's the parents' influence (but don't ask me why).
We also now have student credit now, in case you don't qualify for Bafög money, but unlike consumer credit which has become quite common, student credit doesn't seem to find many friends. People don't want to go borrow 10-30k for a college degree, but they'll happily finance their 25k cars or their 300k+ condos/houses.
I think there are two reasons:
1. Three-tiered school system: German children are separated after the fourth grade and go to three different schools (Hauptschule, Realschule, Gymnasium) and only if Gymnasium graduates can go to universities. In theory this should happen depending on their academic abilities, but in practice it depends on the ability of your parents to support you in school and their interest in your academic career, too. Parents who went to the Hauptschule may think that this is the best way for their child, too.
2. For many jobs you don't need a degree or better you cannot even get a college degree. Nurses, craftsmen and many more professions are trained in vocational schools (which are counted as secondary education in OECD studies). While a US nurse attends a college (as far as I know) and therefore is counted as tertiary educated.
The early separation isn't the greatest thing (although there have also been people switching, or a friend of mine who changed from Gymnasium to Realschule and after 10th grade when Realschule finished he continued on the Gym and actually got his Abitur), but I actually think it helps because different students can learn at different levels and speeds.
Your criticism stands, though, and more recent attempts to reform the school system have introduced "Gesamtschulen", where all students learn together in one school, but pick different courses at different levels. The results are mixed (not as easy as black+white), but AFAIK not that bad.