From: Waipahu, Hawaii
My impression is that the AI nations are spotty in building. Like you, I run my economy right to the edge and rarely have a large bank account. I try to improve all my provinces, particularly those that provide valuable resources.
The AI, otoh, builds a structure/improvement here and there and, often, has very little improvement going on. Their cash just sits there, doing nothing.
My experience is that the fastest way to build up a cash reserve is to win a big war, then, instead of cedeing me provinces, I force the loser to LEND me all his most lucrative provinces for a year. I get all the benefits of owning, stifle my enemy's improvements for a year, and cripple his income for that year, too, while I pile up a large fund.