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^2 with the wing loading of a 737-800 at 98.7 lb/ft^2. 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.
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 to 16. 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.
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.