Education is anywhere from free to really cheap in Germany, and we still don't get many people from poorer families into uni.

I am not German myself, but I am familiar with the system. Please correct me if things have evolved, but...

I thought the post-elementary education system in Germany was a tiered system. University admission requires completing the Abitur exams, but one can only feasibly do this if they've attended Gymnasium, or the "highest" tier of high school. It may be possible to do if one gets very high marks in Realschule (mid tier), along with Abitur preparation courses, but it's virtually impossible if one attends Hauptschule (lowest tier). These schools are not intended to provide university preparation, but instead provide a general education to prepare students for trades/vocational careers.

Whether a child attends Hauptschule, Realschule, or Gymnasium is decided at 9 or 10 years old, and is dependent on performance in elementary classes and teacher recommendations.

And when one considers that a child's educational performance is directly related to both familial socioeconomic status and parental educational attainment, it's not surprising that poorer people are less likely to attend or complete university.

Capitalists' dominant position within the class hierarchy necessitates exploitation of the working class, and this is maintained by fomenting division. This tiered system is just one manifestation of how society can be stratefied and divided.