You are not understanding the way free university works.
Your acceptance depends very very significantly on your performance in high school - there are strict cutoffs based on how you did on your abitur, which in turn relates to a series of high stakes exams and earlier tracking in high school (europe has tracking already in high school where entire high schools are different track).
It's not get a high school diploma and go to university for free. To be a vet, a doctor, a lawyer etc - you basically need to track into these positions VERY early. The good news, they limit the number of graduates through these screenings so the jobs on the other end tend to pay pretty well.
A lot of the posters are claiming you get to go to top universities for free to study subjects that lead to good paying jobs without even taking standardized exams etc. This is totally false.
It's actually much easier for joe blow to become a lawyer in the US then in Europe - including going to law school - including the non ABA schools EVEN if they didn't do well in high school. It does cost money though and for many the jobs don't pay what they would expect or hope for.
Seriously, I wish people would name the top universities without cutoffs - they don't exist.