I like the idea, but the problem is that money does have enough weight in Civ. In CiV, I'd like to see the importance of a good economy increase.
First off, I'd like to be able to rush workers with money. Giving them a speed setting would greatly increase the power of wealthy civs. Highest speed costs the most per active turns, lowest speed is the current maintenance cost (basically nothing for a small to medium sized civ). Workers by default should work slower than before.
I'd also like to see a better way to convert money into hammers, but I don't want a simple "finish for 500 gold" feature to be introduced. Rather, I'd like a more in depth trading system. When one of my cities is connected by road to another, I'd like to be able to spend 1 gold to ship 1 food to the other city per turn. Or 2 gold to ship 2 food, etc. This would allow me to spread out my building capabilities, but for a cost.
This would also improve trading between civs and war dynamics. If I'm at war with civ A, I could go to civ B, civ A's enemy, and buy wheat from him to be shipped to the most convenient city (provided our civs are connected). Then I could use the aforementioned feature to ship it to my unit creating city.
When one city has access to iron, I'd like it to cost something for another city to use that iron resource in a build. For example, if city A has iron, and I build a swordman in city B, I would like the build to cost an 1 gold per 100 hammers or so extra to handle shipping costs. With railroads and better coastal access, the price would decrease.
Maintenance costs for cities should be lowered to compensate for this. Now the cost of colonies could depend on the amount of resources that it needs from the homeland. Coastal cites would reduce this cost, and possible buildings such as large docks or freight warehouses would reduce it further. Colonies would finally be feasible with a good amount of preparation and which places you colonize would be more important (If you colonize an island with iron, you won't have to pay the costs to get it shipped. Optionally, you could just not use it!).
Obviously some balances would have to be performed, but I think this would greatly improve the depth of strategies in the game without over complicating it. Loans, made available with banking, would allow civs to face some of the problems we face today. A civ goes to war but can't afford the shipping costs and the money spent on extra food to support bigger manufacturing cities, not to mention maintenance costs on units, so they borrow from a friendly civ. They lose the war, and end up less 3 cities. Their currency producing capabilities are severely diminished, so they're far in debt with that friendly civ. The loaning civ asks for a city for compensation, but the already bruised civ refuses, and another war starts.
See, a totally new dynamic can be introduced simply by changing the weight of money. It makes sense historically also. How did Louis XIV rebuild France? And how did he ruin it?