it's not healthy- these low carb diets are a fad and unsustainable. Your body, especially the brain runs on sugar. The medical literature has been clear on the dangers of high fat/protein diets in particular from animal products.
Ketosis is making your body do extra work for no reason other than being a way to avoid carbs usually so people can enjoy their meats. Just strip the middle man, which equals stress on the digestive system and go straight for the sugar.
I have observed that the body has a way of letting you know what it is deficient in/of. Sometimes, I get a sweet tooth. Sometimes, I get a taste for meats, etc. I can honestly say that in recent months, I have become a 98% vegetarian. My best advice to anyone is listen to your body; treat it as the temple that it is.
Peace.