Another thing worth noting is that there are two main types of threads on the forums; one is about how to earn and spend miles, and the other is about how to get premium treatment from an airline. In the old world business travellers flew business class and they got business class service -- which was significantly above the service level for tourists in tourist class. After the arrival of low cost carriers the airlines were forced to sell decently priced economy ticket to business travellers. In a sudden a significant part of the most frequent travellers were no longer found in the front cabin(s).
Now, if you are a traveller that is stuck in economy class due to corporate policy then the airline has lost you as a business/first class passenger, not because of your dislike of proper service but because of regulation. In any other business good customers are treated better than less good customers. The frequent flyer programmes doubles as a neat way to rank economy class passengers, and to give back some of the business/first class privileges to those who are good enough customers.
And then the win/win situation is obvious. I choose to fly with one airline (or one alliance) instead of five different ones simply because I seach recognition as a good customer of an airline, which in return will spare me the long queues on check-in and give me a nice chair and a drink while waiting for their delayed flight.
My best guess is that the most important reason to keep the frequent flyer programmes is centered around customer-relations management, and not around having a profit center around a fake currency.