> There's something very contrary about expecting payment/compensation for FSF software.
No, there's really not, because free software is about freedom, not price. C.f. https://en.wikipedia.org/wiki/Gratis_versus_libre
> Or don't I understand the FSF at all?
I think that's the case. Read https://www.gnu.org/philosophy/free-sw.en.html for more about the Four Freedoms: to run, to study, to distribute copies & to distribute modifications.
The FSF (for all its faults) has done a lot of good in the world, and companies like Google & Amazon owe it a huge moral debt. They are under no legal compulsion to pay it a single cent, but it's fair to say that without the Free Software Foundation there would be no modern web.