Historically, AC motors were used for single or double speed elevator machines on the grounds of cost and lower usage applications where car speed and passenger comfort were less of an issue, but for higher speed, larger capacity elevators, the need for infinitely variable speed control over the traction machine becomes an issue. Therefore, DC machines powered by an AC/DC motor generator were the preferred solution. The MG set also typically powered the relay controller of the elevator, which has the added advantage of electrically isolating the elevators from the rest of a building's electrical system, thus eliminating the transient power spikes in the building's electrical supply caused by the motors starting and stopping (causing lighting to dim every time the elevators are used for example), as well as interference to other electrical equipment caused by the arcing of the relay contactors in the control system.
Why were AC motors used? (If the question is unanswerable, say "unanswerable")
cost and lower usage applications where car speed and passenger comfort were less of an issue