Honestly, it's not just capitalism. Education is anywhere from free to really cheap in Germany, and we still don't get many people from poorer families into uni.
I see the main problem here as a sort of class divide between people with university degrees and people without.
For example: if you work in a public library and don't have a uni degree you will never get more money than salary level 9 (4k/mo) just having a degree and not doing any more/different work more or less instantly puts you on 12 or higher (6k+)
This I think understandably makes people without uni degrees kind of resentful of those who do have them. And if you grow up resenting a certain group of people you are much less likely to join them.
So, no. "Just" getting rid of the cost won't magically get these people into higher education.
How so? In particular how would you compare it to apartheid or India's old caste system?
Making big jumps in income is mostly luck based (building a company and getting funding for it), but is not inherently bound to some external property, like where you live or who your parents are.
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.
It is absolutely possible to get to university after only finishing Hauptschule. You just need to go to BOS after finishing your apprenticeship and then you can achieve a fachgebundene Hochschulreife (maybe even allgemeine, im not sure) and attend University. Few people do it, because the desire is not there, or maybe not the tenacity to study further after already having trained for a job. Also you get Kindergeld and Bafög while studying.
And when one considers that a child's educational performance is directly related to both familial socioeconomic status and parental educational attainment,
This is true and criticized by PISA every time.
I think it has a lot to do with how much the parents value education. east asian immigrants are famous for how much emphasis they place on education and as a result get into university. The only thing that would help immediately (i.e. does not require behavioral change for a large portion of the population) would be to separate kids more from their families via Ganztagsschulen, to weaken this influence.
Do you know Aladin El-Mafaalani? I think this Interview (in german) with Jung&Naiv is totally worth to watch for everyone that is just slightly interested in that topic of the german educational system, its flaws and how to improve it.