It has its own blood supply that is compatible with or matches the patient. The immune system recognizes the graft as its own self and doesn't try to reject it or take it out. The autograft also has a better blood supply than an allograft so fusion is faster.
There can still be problems with an autograft. Pain at the donor site is a common postoperative problem. Researchers are looking for the ideal graft that will give a high rate of fusion with a low rate of complications.