I will chime in here. I have not hunted an elephant with a bow - I was denied a bow permit in Zimbabwe on my elephant hunt so I had to use a rifle. I do have a bow capable of taking an elephant. It is a 90lb draw Mathews Monster Safari (28.5" draw length, 1,250 grain arrow with I think 116 foot pounds of kinetic energy).
I have used this same bow on Cape buffalo, North American bison as well as giraffe. I think a giraffe is a tougher animal to take down than a Cape buffalo, but just not as dangerous. My last giraffe was the first one I shot broadside and it went down with 1 arrow after running about 200 yards.
I have taken 3 Cape buffalo. All three went down with just one arrow. The farthest any one ran was 60 yards. Only one of the three even lived long enough to give a death bellow and that one gave me three of them.
It is not legal to hunt an elephant with a bow currently in South Africa or Namibia. It is legal in Botswana, Mozambique, Tanzania, and Cameroon. I have been told it is not illegal in Zim, but good luck getting a permit because most places in Zim will not issue the permit. I am not familiar with the regulations and legalities on bow hunting elephants in other African countries.
We can go round and round on the ethics of bow hunting DG and it is not likely to change much as ethics are a personal thing. For every rifle hunter who feels it is unethical to hunt that animal with a bow, I can find 10 city slickers who think it is unethical to hunt, period. Such debates do not accomplish much. What I will say is this: most people, including rifle hunters, have no real appreciation for how lethal an arrow is. True, they don't have the stopping power of a rifle, but I think they are at least as lethal and quite possibly more lethal than a bullet.
Now, on to other things - most of my hunts with a bow do not end with a gun. Very few of them, but some have. That said, a lot of hunts with a gun also end with a gun and sometimes another person's gun. It is just very difficult to get a second arrow into an animal unless it is essentially walking dead. I think a fairer comparison would be to see how many animals go down with one bullet vs multiple and compare that to how many animals go down with one arrow vs having a follow up shot (of any kind). I think we might find the rifle hunting crowd a bit surprised by that result, although I might have some bias as I am just using my personal experience as a guide.