I don't see them working on making it cheaper for the common person out of the goodness of their heart. And I see their desire to keep their power as stronger than their desire to worry about healthcare costs.
Life isn't some game of throne that incentivized the creation of bloodthirsty ruthless power mongers except in some of the most dystopian place on earth.
Maybe I'm super cynical and pessimistic, but if the cure for aging is found, I don't see it being made widely available, ever, for simple reason of power and politics. Humanity isn't at that point, and likely never will be.
Economic and technological force might make such attempt at control a pointless exercise, especially since a cure will likely be made public by scientists.