The primary design driver of a commercial airliner wing is efficiency, and second to that is speed. While delta wings are good at high speeds, they are not very efficient. Also, while an airliner should certainly be maneuverable, they do not need to "do a barrel roll" or make 9G turns light a fighter jet.
It was mentioned that delta wings have a large surface area. This helps to distribute the weight of the aircraft more, which leads to a low wing loading. This is one factor in the higher maneuverability of the delta wing. Compare the wing loading of the F-15 at 73.1 lb/ft^2ft2 with the wing loading of a 737-800 at 98.7 lb/ft^2ft2. The delta wing allows the F-15 to have lower wing loading and thus much more maneuverability. The design also keeps this large wing area to a low wingspan, which means that high-G maneuvers cause lower stress on the wing. Airliners have plenty of maneuverability with their current configuration.
This large area and high speed performance is at the expense of efficiency. The lift to drag ratio (L/D) of an F-15 is around 10, while the 737 gets closer tocommercial jets get over 16 (see this table for some examples). This shows the huge advantage that a non-delta wing has at subsonic speeds. Modern aerodynamics have allowed commercial airliners to reach high subsonic speeds (Mach 0.8-0.9) while remaining very efficient. While fighter jets use aerial refueling to compensate for burning more fuel, this would be a bit unrealistic for a commercial aircraft.
Low speed performance is also a factor. Both wings are able to use flaps and slats, but landing speeds for fighter jets are generally higher than commercial aircraft. Being better suited for high-speed flight, delta wings are less effective at low speeds.
As far as maintenance is concerned, there are fewer differences. Since the wingspan would be lower, this would put less load on the wings. Reducing the load could be turned into a maintenance advantage, but there are many more factors in determining maintenance cost.