What profit do you really think ANY private investor, national or foreign, would EVER see in spending tens of millions of euros to run a one off grand prix in Portugal? No one private entity holds enough power to actually profit from a GP here.
That's like saying "the state should stop paying for research on rare illnesses, it's time the private sector does it". It's completely ass backwards.
So lets leave it to Arab/Asian/African rich countries to finance. Let them host the GP's. It's not like F1 is as public service like research on rare illnesses.