According to at least one source (Hard Landing: The Epic Contest for Power and Profits That Plunged the Airlines Into Chaos by Thomas Petzinger) the prime reason American introduced AAdvantage and unique numbers was because they wanted to be able to track individual travelers booking and buying patterns and a phone number was not a unique enough identifier because in too many cases it was either the travel agents' phone number, or a corporate office main number or any number of other cases where the same pre-cellphone phone era number was shared by "several" to "hundreds" of different people.

The miles were just to incentivize people to go to the effort of making sure the number was reflected in the reservation