Western vs Eastern State Sponsored Education
What you are describing is a very common phenomenon in Western style public education as a whole, not just Germany. Despite socialized college education, Germany is still by-in-large a capitalist country in the way that it manages its public services. In most Western school systems, the government pays for tuition and grants, not directly for the operating costs. When the government only pays for tuition, it means that the schools still need to compete for funding, and the most important metric for determining funding is how many students you serve.
For example, if you have the facilities and staff for 5000 students, but only 3000 pass the entrance exams because they are so difficult, then the school is still stuck paying for thier larger facility but with less income; so, it is in the best interest of the school to always fill every available seat. So, to balance the budget, state sponsored universities set thier entrance requirement to the minimum it takes to guarantee 100% enrollment, not based on what it takes to complete the coursework. In the inverse case where a school has the facilities and staff for 3000 students, but they get 5000 who pass the entrance exams, then there is a financial incentive to accept over thier capacity, and use some of the extra funding to expand thier facilities until they can host 5000 students. In this way, there is a supply-demand function in the way Western schools operate that encourages them to always accept the maximums number of students that they can and to grow to the capacity of the market.
In contrast, Eastern states operate based on the Communists economic model in which schools are given a fixed budget and are required to function within it. So, if an Eastern school is budgeted to serve 3000 but has 5000 applicants that should be able to complete the coursework, then they are not able to collect 5000 tuitions from the State and use the money to expand the school system. Instead, they can only accept the best 3000 until the government chooses to expand thier funding. On the inverse, where they have 5000 seats and only get 3000 applicants that can pass the entrance exam, there is typically no penality for only accepting those 3000 applicants because they are still doing thier jobs within the budget allotted.
This puts the financial incentive for many Eastern Schools to operate by accepting as few students as the government will allow them to whereas Western Schools operate by accepting as many as are allowed.
A second major difference is the contrast between Populist Socialism and Communist Socialism. Communism Socialism which is most popular in East Asia is based on the original Marxist view that "From each according to his ability, to each according to his needs". This means that Communist Socialists have no expectation that all people have the same abilities, opportunities, and needs which leads to a strong cultural bias toward only uplifting those who show merit. In contrast, Populist Socialism which is the primary form of Socialism found in Western Nations, is based on the view that the government is responsible for making sure that all people have the same opportunities regardless of thier current ability and background. This fundamental difference has influenced the goals and laws of the Western vs Eastern systems.
There is also a more recent cultural element to German education that they try to make it as non-competitive as possible. Competitive learning environments are experimentally shown to reduce the effectiveness of education, and Germany is among the top nations when it comes to applying this principle. In Germany, there is a much greater belief that a person can fail one test, and still move on to achieve great success down the road, even when compared to other Western cultures. So, while East Asian countries have built thier public education system around minimizing how much they need to invest, Germany has built thier system around maximizing the possible return on thier investment.