We don't need fees. If the miners aren't getting enough from the coin they mine, they can sit on it, and supply and demand should raise the price.
You're only considering newly mined coins, not the 17+ million other bitcoins in circulation. With each passing day, miners comprise a smaller and smaller portion of the total supply. Since they don't dictate the supply, the market doesn't move to their whims.
In your vision, what do you expect to happen when block rewards approach zero?