The university departments get different amount of money depending on the amount of students they have, but this money cannot be spent freely (e.g. on increasing professor's salaries), but must be spent for education-related things like hiring more TAs, which is something that departments that get more students need to do anyways.
The professor salary is pretty much standardized (per the TVL), which does allows for sur-pluses in case that the responsibilities justify them, but university "students" do not play a role here. Things that affect these are, for example, having larger management-related responsibilities. For example, a professor with 4 PhD students and 2 postdocs gets less money than a professor with 30 PhD students, large experimental facilities, 10 mechanics, 5 middle management personell, ... adding up to 60 people under supervision.
So while I agree that the universities do have an incentive to grow the number of students in STEM degrees, the professors do not really have a big incentive to make the degrees easier.
The professors that "get rich" in Germany have large consulting companies on the side to which they try to attract the top talent, so if anything, the incentive is to produce more top talent. This can incentive them both ways, making things easier to attract more students to get more students in their companies, or making things harder to filter out the bulk from the top talent. But that's just supply and demand.
Entire departments are built on this principle.
On top of that, there are no limits on how many times you can retake a class, it is not unusual to be stuck with the same class for three or four years until you manage to pass.
There's no way you can generalise about incentive structures like that for an entire continent.
In my country, only public universities exist and the incentive structure is decided politically. Currently, universities get paid a certain amount for each student that graduates, but they are also deducted some set amount if the student doesn't graduate within a specific amount of time. In addition to that, the sum of money gained from a single STEM student is double that of another kind of student, so the universities have quite clear incentives to promote their STEM degrees.
Obviously, an incentive structure based solely on passing students must also inspire grade inflation. The current structure highly incentivises making STEM degrees easy to obtain. Whether that's actually the case, I can't say, but the structure certainly encourages it.