1) Granted, German tax payers are paying for German universities. But do you really think that tuitions in the US reflect the actual cost of operation of colleges? Mathematically speaking, Harvard generates enough money to provide free tuition. Are they gonna do it? No, cause in the US you pay for a brand.
The fact that schools are public means that there is no price inflation due to image, brand, PR, etc. You pay what it costs to get education.
2) It is not just about throwing money through the window. It is an investment to get young educated people, some will go home but some will stay and use their education to create jobs.
But do you really think that tuitions in the US reflect the actual cost of operation of colleges?
I certainly won't defend the cost of a college degree in the United States, but that's not my point. I object to this being called "free" since the cost is merely transferred from the individual getting the education to that country's taxpayers.
If I were a German taxpayer, I'd likely be fine with helping support such a system....if used by my fellow Germans (longtime residents or new immigrants). Subsidizing foreigners who will likely leave the country after graduation? Not so much. It strikes me as rather parasitic.
According to the BBC article cited in the post, 50% of foreign students wind up staying in Germany. Germany suffers a fair amount of brain drain to the US. They're more than happy to have some of our more enterprising students by way of compensation. Certainly, there would be a financing issue if huge numbers of Americans head over for a free ride, but we're a long way from that point.
And my second point addresses that. The German government thinks it's worth it to attract young students and hopefully see them stay long term and help the economy. This system is not unique to Germany, a lot of European countries work the same way.
You're 100% right, nothing is free.
However, same quality education might be significantly cheaper in some places - e.g. medium-tier uni I went to in Canada charged ~$7000/year in tuition (back in 07).
Somebody is footing the bill, just not apparently the student.