I'm a nurse practitioner with over ten years of experience in orthopedics. This idea is great as a concept, but is unworkable IRL. First there is the problem of swelling as mentioned by others- it often takes days or even weeks for the swelling to go down enough for a permanent cast to be placed- we use splints and ace wraps until then. Second, 3 plus hours to print the thing is not feasible in the ED or in a doctors office.
The biggest problem I see is that many fractures are unstable. This means that the muscles pull the bones in such a way that the broken ends of the bone won't stay properly aligned unless they are held in position. This is usually fixed by one person holding the limb so the broken ends line up as well as possible, while another quickly applies the padding and casting material (plaster or fiberglass) and molds it to shape so that it will hold the fracture together until the bone heals. Limbs sometimes have to be bent to a specific angle and then casted as another way to prevent the fracture from falling apart again- for example, if you broke your leg, just above the knee, chances are you would show up at the ED with your leg bent. We would have to sedate you, pull your leg straight, and then apply the cast. The whole time, some poor schnook (sometimes me...) would have to keep pulling on the leg, holding it straight, until the plaster or fiberglass sets.