Well fed cats might be a tad lazier and rabbit is real prey compared to the little critters. The neck biting is natural behavior it's the concern of what it can lead to. Even if this situation works out it's important that everyone realize that for every one that works there is one that doesn't. Aside from the rabbit being injured their back legs are extremely powerful and could easily rake a cat up severely.The hunting instinct is in all cats, no matter how well fed. The Ladies never lack food, but any lizard, moth or bug spotted has at least two cats on it. The one that ends up with the prize growls at all the others to try to keep them away, but it can become a free-for-all to see which one can frolic it to death.
The neck biting I see is usually just a way to show dominance. I see all of them biting and being bitten. Usually, the biter slobbers on the bitee leaving wet fur. Yuck.