Not only that, they took a lot of money in exchange for that "free" eduction -- often from people who didn't even use the service. So no, they don't have a "stake" in the products of anyone's mind. That's repugnant.
What government are you talking about? Does "free" education implies the obligation to give all your life work output to the government? This seems very foreign, please name at least one country that implements those ideas.
I was merely speculating, but I think Hungary might set the precedent.
Alternatively, whenever you buy storage media (DVD-R, HDD) there is a surcharge that goes to authors. That's all done on the premise that this media will be used for piracy.
You already pay tax on information when you watch Netflix or licence a patent.