In other words the whole system will stabilize on a reward level appropriate to justify the amount of mining. Difficulty, mining reward and bitcoin value feed back to each other.
Yes but the question is what happens when all the coins have been mined?
Fees are part of the mining reward. If no one pays fees, bitcoin mining collapses, difficulty collapses, value collapses. In the process someone will start to dispose of their bitcoins in anticipation of the crash. They will pay fees to get the transaction included. The system will eventually reach an equilibrium where enough rewards ((block reward + fees) X bitcoin value) will be provided to justify mining at a given difficulty.
As long as the value of bitcoin is high enough, even a satoshi in fees will ensure mining continues. Bitcoin being valuable is a result of it being in demand. If it is in demand it will change hands, there will be transactions.... etc etc.
Of course, if no one uses bitcoin, i.e. no one uses the network, it will die. If no one pays fees, bitcoin would be very easy to mine.