It would make things too complicated, because everyone would like to stay alive, thus, when they get to near 0 HP, they would make themselves "God-like", avoiding every attack, until a healer comes by, and heals them, or until they can buy another Vulnerary.
I wouldn't do it anyway. I'm not updating that stupid signature every time i get hit. Just roleplay like a normal person... and get hit every now and then. Heck, I can see some of us dying, this is Fire Emblem, people die frequently.