Is it unhealthy or not really depends on what you eat. Eating a lot of meat puts you at higher risk of cancer. There was a study not so long ago that looked at mortality in a zoo, and carnivore animals, especially those eating mammals (so beef, pork, lamb, ...) up to 40% of them were dying of cancer, compared to the herbivores. Fascinating study if you want to read it www.nature.com/articles/s41586-021-04224-5
Carbs are not only a source of energy, they also have a structural function. . They give shape to a plant which lacks a skeleton. By cutting carbs , you cut plants, and a great variety of types of fibres. Fibre, especially viscous fibre, will regulate cholesterol.
Most importantly however, you cut phytochemicals. There are tens of thousands of them and they carry protective functions and also regulate your genome. By cutting a lot of plants, from carrots to pears, you miss on the protective functions of so many compounds. On the body, but also brain and mind. Studies after studies how ADHD incidence can be reduced by a Mediterranean diet in children and the same is true for dementia incidence. Multifactorial of course, but within our reach.
And don't even get me started on the microbiome. A healthy gut likes carb, oats, legumes, whole grains, a lot of fruits and vegetables.
So to answer your question, you need to look at what you eat. Other animals three times a day (eggs for breakfast, chicken at lunch, fish for dinner) , hum.... not so good. A big lettuce, rocket and kale salad with avocado, prawns, nuts for lunch, a curry of low carb veggies stir fried for dinner, yes, that healthy.
In the end, it isn't about was you leave out, but what you put in your body.