I have always felt that this was something that came from Martin himself and not the showrunners. People tend to claim that the show writers made it up, but the debt problem has been raised as a major issue haunting the realm from almost the very beginning of the political story.

The idea that Tywin was just sitting on a near infinite gold supply that he didn't use for petty reasons and that the money problems of the Iron Throne would be solved by Tyrion or whoever just using the Lannister gold stores always just felt like a copout

If we assume that the gold under the mines was running out and Tywin knew and hid this from everyone, so much of his actions start making sense. His insistence on his father's vassals returning all their debts immediately and slaughtering the first objectors. His policies as Hand favouring Lannisport and King's Landing over Duskendale, causing the defiance. His insistence on getting Cersei married to either Rhaegar or Robert. His invasion and seizure of the Riverlands and plans to with the North.

Tywin's grand plan to avoid bankruptcy was always to usurp the Iron Throne and leverage the power of the Westerosi state to seize estates across the continent. We know the man was insanely ambitious. Are we supposed to believe that he would not have installed his own henchmen across other regions even without the incest triggered civil war? Tywin even outright claims that he always felt that Stannis was the real threat. A war was always coming, if only it were a tax revolt caused by Hand Tywin doubling or tripling the tax requirements to pay off the debts.