The unavoidable truth about game theory is that if you change the game enough then the outcome will be different. In fact, that is the whole point of having a "game theory" in the first place. Nowhere is it written that a game is unfixable. This is just a pseudo-mathematical fantasy of a certain class of unimaginative and uneducated dogmatists.

The issue is what it takes to fix the game.

In this case, we effectively have to START by convincing the people who would be disempowered by a change in the game that they will be better off allowing the change in the game than by not allowing it.

And it is ALWAYS hard to sell people on the notion that they will be better off if we take privileges away from them.

(Not impossible. England's Parliament extended the vote to the common people, in part, because a well-regarded and rather conservative member of the body wondered aloud what would become of the existing members of Parliament if the common folk decided to take that privilege by force.)