Miners mine because they receive an incentive to do so.

Currently, the 25 BTC block reward is the primary incentive.  The transaction fee will only become an issue when the block subsidy approaches zero.  This won't happen for several decades.  However, when it does, transaction fees will need to provide enough incentive for miners to continue mining.  By this time, it is assumed that Bitcoin will have grown to the point that there will be millions of transactions with small fees attached to them, and the sum of these fees will provide an incentive for miners to continue mining (e.g. one billion 1-cent transaction fees total $10 million in incentives for miners).

And, even if BTC becomes so valuable that .0005 BTC is worth a lot relative to fiat, the transaction fee can be reduced.  All that matters is that a balance is achieved wherein miners are happy with the incentives they are given for their work, and users are happy with the low transaction costs.