Drew brilliant question! I love these questions because they are what drive discovery.
This is a rather tough question and I think you will have to search for a professional geneticist or biologist.
I will give my opinion given my somewhat limited experience and knowledge working in the medical field.
In fact, allografts (bone transplants) and marrow transplants are performed all the time and they typically come from recently deceased individuals. When you ask "why can't we transplant...from someone who died" I am guessing you mean someone who recently died. You can't transplant anything from someone who has been dead for any significant period: the necrosis (tissue death) would be so bad that the function of the organ or body part would be gone and it would be fatally toxic and filled with bacteria.
A complete bone transplant, well, that's a fascinating question. I think it is possible...I might have to Google that. It's hard to envision a scenario where an entire bone would have to be transplanted. Bone tissue is so regenerative during a person's lifetime. I know of a case where a patient had a head on traffic collision with a semi (tracker-trailer) and was missing FOUR inches of his femur. How he survived is incredible in itself. Nonetheless, they surgically put the femur back together and placed an invasive device into the femur that would stretch the bone over the course of about 6 months causing it to grow.
One of the major set backs with doing transplants is that the patient has to take immuno-suppressors for the rest of his/her life. Even though you can get patients with similar genetic history, because those biomolecules don't match exactly with the patient's genetic code the immune system will attack it as a pathogen (foreign substance, ie. bacteria). Thus, the patient will be much more vulnerable to infection and sepsis (systemic infection). Therefore, it is always better to use the patient's own resources.