I would have no health concerns with a carnivore diet, as long as some raw/rare meat was consumed for vitamin C.
I do a combination of Carnivore/Paleo/Ketogenic diet. I eat blueberries so I am not a Carnivore and I eat yogurt so I am not Paleo and I bounce in and out of being Ketogenic. I've been doing so for over twenty years and a few years ago my physician told me that based upon my test results that there was no reason for me not to live to be 100. Not to say that I don't have problems. I've had at least 8 blood clots in the last 35 years and numerous kidney stones in about the same time frame. Five years ago a blood vessel in my brain broke and almost killed me. I've managed to recover from all those and yesterday I did a 100km bike ride.