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It has essentially no fat. So while "no nutritional value" is not true, you can actually starve to death eating rabbit only.

Same goes for any number of lean game creatures. But all you need to do is introduce some carbs into the mix, and you won't get protein poisoning.
https://theprepared.com/blog/rabbit-starvation-why-you-can-die-even-with-a-stomach-full-of-lean-meat/

man can't live only on protein

but it doesn't mean protein has no nutritional value