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. At least until the people stop trying to make trades.
This should work in theory, but in this scenario you're basically expecting Bitcoin to continue to keep grow indefinitely to be able to offset the continuously halving block rewards. Once that stops being true, we risk hashrate dropping and compromising the network's security.
I would really prefer for fees to be negligible or even zero, but that poses problems to the economics behind the system.