Fee rates will tend to go down with competition, since even a minority of miners willing to accept a lower fee will not unreasonably delay a transaction's acceptance rate. E.g. if 1/6 of miners are willing to accept your fee the time to get 6 confirmations is doubled on average. That way most users will only pay a fee that enough (but not most) miners will accept. These miners will make more profit (from transactions the majority reject) while only contributing a minority of computer power. So the rest of the miners will have to also accept these low fee transactions, and there is really no motivation for them not to, as the real cost to include a transaction is negligible. But then some miners will try to get an edge by lowering fee requirement even more, and the cycle continues.
  Once fees go way down, there is only profit in generating blocks if you can do that easily, but that will destabilize the whole BitCoin concept.
  The only thing that can save the day is the minimum fee of 1E-8, since there is no motivation to include a 0 fee transaction.
  My suggestion is to change the way block rewards work, so that mining goes on practically forever, and not stopping
~2138. But that's for another topic.