When I come into threads that I consider a very BAD idea, I can usually at least SOMEWHAT see where the poster was coming from. "They mean well, but they are overlooking some very key facts..." I fail to see how the OP could see this as a good idea, but rather than laughing in the OP's face... I will explain.
If you take out all gil and the ability to trade items, you will essentially turn this into a single-player game with a multi-player component. You would work with others for dungeons and instances and that is it.
MMOs have a thriving economy. I would argue that this is one of the staples of an MMO. Crafters and gatherers have their place. Take out the ability to even GIVE items to another person, and crafting/gathering becomes something that EVERY SINGLE PERSON must do. How will you eat food? Everyone will have to level culinarian. What about furniture? I guess people will have to level botanist and woodworking. Any mage will need to level weaving. Heavy armor wearers will need blacksmith. If you want to do anything, you must be self-sufficient... which brings me back to my original point: taking away money and the ability to trade items will basically take away the MMO component. It will become like many other games that have an 'online' mode to help you get past certain objectives, but that's it. Sure, everyone could 'roll' on certain items but helping each other outside of that is next to impossible. Who will meld your gear? Who will make the food for runs? Who will build the furniture for a house? Who will make the armor?
If this isn't enough to convince you, consider Square Enix's perspective: MMOs are designed to keep you playing, and often. When you aren't grinding the latest content (You can only do all five turns of BC once a week, after all), you need to occupy yourself another way. If making money becomes pointless, either you grind for yourself or limit yourself to the dungeons. The community aspect of MMOs becomes stale and dry very quick. I don't know about the rest of you, but a huge part of why I play MMOs as opposed to single-player games with an online component is because I like helping others and working together. I'm a botanist, so I'll gather materials for food. Then a cook in my FC will turn them into food. The food is then distributed to FC members before a raid so that people don't have to buy it themselves. Everyone contributes their help in some way and it becomes a community.