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 which will change the economy of our society for the next hundreds of years.
I guess no one will think about setting up miners to earn 1 satoshi (divided to all the miners in a pool!), but the fees, which are now at about 1-2 BTC per block.