I've seen the AI store up thousands in gold in several of my games. I once saw Bismark store up to 10,000 in gold before.
That's not common, because if the AI CAN spend money on something it thinks it needs, then it will. As long as the AIs remain friendly with each other, they'll buy Research Agreements whenever possible. And if the AI is in a war and needs another unit, he'll generally buy it.
It is annoying to see the computer save up all that money then spend it all on a diplomatic victory in the end while I'm sitting back shooting for a technology victory.
Then that means you
lost, and the AI did what it was supposed to. If the AI had enough income to be able to buy a diplomatic win outright, then it meant that he was strong enough economically that he SHOULD win and that you were never in the dominant position anyway. And that means you need to start looking into countermeasures; bribe a few city-states of your own, instead of sinking all of your money into rushed units and buildings. Or conquer a few city-states yourself (since the number of votes needed does NOT go down as city-states are conquered, so take out enough of them and a diplomatic win becomes impossible).
The cultural and diplomatic victories are in the game for a reason. A civ that's a runaway tech leader, or is dominant militarily, needs to pay attention to those other factors instead of just beelining for its own preferred victory at all costs. Just because you're getting close to a science win doesn't mean the AI shouldn't be able to try winning some other way.
Now, if you think a diplo win is just too easy in general, there are other ways to mod that: reducing the effects of bribes, increasing the number of votes needed, increasing the frequency at which city-states offer "quests", and so on. But don't blame the AI for doing exactly what a player would do if he were going for a diplo win.
Tight money supply would lead to inflation as less money is chasing the same/increasing amount of goods being produced.
Only if you assume that the gold we're talking about here represents the entirety of an economy. It doesn't. The gold you're generating really represents the amount of money the government has to spend on whatever additional projects it thinks it needs. As the U.S. has shown for decades (until the last couple of years), it's easily possible to have a strong economy while the government has a massive deficit, as long as the citizens continue to gain and spend money. A negative income doesn't mean a shortage of money throughout your empire, it just means your government is spending more on infrastructure than it gains in taxes; as long as there's another nation willing to loan money to cover the deficit, everything's fine.
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Bottom line, I've told you the mechanical problems with adding this into the game in a way that the AI would be able to handle. So no matter how much you like the idea, it just won't work, because it'd give a human player (who knows about the system) a huge advantage over the AI. When we get the DLL that'll change, but until then...