Theory about Tachibana's Past
What if Kanade was in a coma, waiting for her heart surgery? While she is in a coma, she is in a dream state where she is in the same world as Otanashi. (KANON SPOILER: Like in Kanon when Ayu was in a coma for seven years that goes into an astral projection and met Yuuichi.) Isn't her purpose of her staying in the Afterlife world was to thank Otanashi for his heart?
This is just my theory but please correct me if I'm wrong.