I agree with Kremmen. The logistics of keeping track of the dollars spent is much more difficult than keeping track of miles flown.
While it is relatively easy for an airline to determine the fare for customers that purchase a published fare, there are also alot of non-published ticketed fares out there. The airlines do not how much the customer paid for these types of tickets: Priceline, bucket shops, wholesale, bulk rate, tours, contract rate tickets, etc.
Even if the airline were able to accurately determine ticket prices, I think they would have originally used miles anyways since it is more attractive for marketing purposes. Customers do not want to be constantly reminded of how much money they are spending on airline tickets. Wouldn't you be disgusted to know how much money you're actually paying for airline tickets? For many of us it is in the tens of thousands. Who wants to be constantly reminded of that?
On the other hand, customers are always interested to know how many miles they've flown. They would rather think "I flew 32,768 miles this year! Woohoo!". Nobody wants to think "I spent $12,332 on airline tickets this year! Woohoo!"
Face it -- miles flown vs money spent is just more marketing sexy. Yeah?