I should have gifted Currency to the AI, so that I could sell them techs for a few coins now and then. But I can't follow your idea about trade routes. You enjoy as many traderoutes per city as your tech and civics and WW allows. It can also be limited by the number of AI cities, if there aren't enough of them then some of your traderoutes will be internal and thus less profitable. The value of each traderoute depends on the size of the two cities involved. The number of trades routes that the other civ cities can enjoy does not play any role in the equation.
Nearly every one of my trade routes was internal, I had 4 or 5 per city by the end of the game, and I had 10 cities. I've heard that the trade routes I can set up with other civilizations are also limited by the number of trade routes the other city can support. This seemed to be true, because my trade income went up after gifting Currency away, but I'm not really sure that it wans't a result of soemthing else.