My housemate was hit by a car. left leg broken. had surgery. given crutches and a prescription. no cast. why would a doctor not provide a cast?

Various reasons : If there is an open wound or incision, it is definitely better to leave it open for healing & to prevent infection. If they did surgery, they probably inserted a pin/plate &/or screws. These provide better stabilization than a cast can. They may also be waiting for swelling to go down. Finally, i suspect he/she has been told to take it easy. Please follow docs instr & don't be afraid to ask ?'s.

Fracture stable: If the friend had a fractured tibia or femur often the surgery entails placing a rod in the bone. The fracture is stabilized and no cast is necessary.