Earning by fees will be the motivation to run miners long before the last few Bitcoins are mined. The last block reward will be 1 Satoshi for about 4 years.
Just thinking about what will be the price of BTC by then. 1 satoshi for 4 years is insanely low if the price of BTC hasn't reached an insane figure of numbers. I won't be there by that time but I am happy with what I have right now and felt lucky to see the raise of giants.