A good primer, but there are some points I think should be made.
Inflation in world history is a tool used by rulers to gain command of additional resources:
But they didn't really understand that they were using it. They thought: "Hey, free money!". In that respect I suppose CivIV inflation is perfect.
And not just rulers. Gold is pretty much worthless, and yet any yahoo that finds a gold mine can suddenly buy anything they want.
Can you imagine what would have happened if alchemy actually worked?
Effectively, inflation acts as a hidden taxation of the productive output of all members of society who use money to conduct business.
But CivIV; no CivN, or as far as I know any of it's clones; actually has a visible taxation. Everything the society produces is available to you as the player. One assumes that the player isn't actually a ruler, but rather the "guiding spirit" of the civ.
The upshot of all this is that you, the civIV ruler, should have the choice of when to 'inflate' or not. Inflation has the short-term benefit of giving you control over more of the existing real wealth in your empire, at a long-term cost of higher future prices and lower overall productive efficiency. So this should be something you can choose to do, or not, and set the 'rate' of inflation as well. In game terms this would amount to simply setting a percentage value of 'inflation'. This percentage is applied to the current gold revenue and given to you every turn as additional free gold. However, in simplified game terms approximating reality, the penalty is that prices of everything (production cost and upkeep cost) will increase by this percentage + a small inefficiency penalty. So if you set inflation to 20%, 20 or 30 turns down the line, the cost of everything has risen by 20%, plus a nominal penalty of say 10%, for a total of 22% increase in shield cost to build anything and gold required for all upkeep and purchase costs. The benefit is that before the general cost increase hits in full force, you have a few turns (to be determined as befits game-balance, probably a variable value depending on game-length) to spend all that extra gold you got by cutting it with 20% pot-metal (or by running the printing presses, as we do today) at CURRENT prices. Ultimately what kills you is the accumulation of the nominal penalty so that the empire which inflates is able to engage in more activities short term, but pays an ever-growning unit maintenance and upkeep penalty which the non-inflating civs don't have to pay.
Needless to say, inflation is a short-term expedient which is inherently wasteful (decreases economic efficiency in ways beyond the scope of those post) and prone to spiraling out of control: the ruler must continually inflate in ever-greater amounts to reap additional benefits while simultaneously paying for the ever-increasing support costs precipitated by prior inflations.
Since the commerce output of, say, a town presumably represents actual productivity, in time it should adjust and produce more of the less valuable currency. Only by continuously having a large inflation would you actually hurt your economy. The same effect could be acieved by allowing you to pillage your own improvements for

.
Presumably that's what happened to the Romans. They expanded their currency supply so much, for so long, that the economy never got a chance to recover. Because they didn't know better, because, as you say, it is a
hidden tax. They couldn't see it themselves.
In short, before inflation is added as a hidden tax, we should add a visible tax.
Also, in civilization, production

hammers

is largely unaffected by money

gold

. It is completely unaffected by "inflation", since "inflation" only applies to upkeep.
I think the most fundamental change needed is making money a part of the game, rather than an optional extra like it is now. Master of Orion III did a great many things, many of them wrong. One of the correct things was making money a part of the economy.
In civ terms, to build a unit or similar, you have to pay the

cost in

, and you can't spend more than the numbers of

produced by your city per turn.

comes from taxes, rather than

.
Edit: I've no idea why the second quote is messed up.
Edit: Thanks to Honor for solving the quote mystery.