Actually, its a really interesting idea. There would still be markets that could be played, although it would be difficult to implement. Somebody has some items they want to "sell" (trade), and... That's the difficult part, right now you can just exchange your item for gil, which you can then use to buy things you need. If you trade your one item for something specific, it would be difficult to "sell", because of the small amount of people who want your item AND have the item you need.

I really like the idea (maybe in another game, gil is a staple), but I personally think people would just use certain items as currency, thinks that are moderately difficult to obtain, limited supply, etc etc.