It is possible to live completely without vegetables. The Inuit did it, the Masai do it, and many isolated tribes and island peoples discovered over the last fifty years were eating only protein and fat until they met the modern world and changed their diet (acquiring the “Western” diseases in the process).
The classic experiment was performed at Bellevue Hospital in New York in 1927 on two explorers, Vilhjalmur Stefansson and his friend Peter (?) Andersen. They had spent a few years among the Inuit in Canada, eating their traditional diet, and no one in the New York medical establishment believed their story, so several doctors challenged them to live only on meat and fat under supervision for a year. They did it, living at Bellevue hospital (locked up, at first), and the only problem they had was one day several months in, when they allowed themselves to be persuaded to eat lean meat and no fat. They felt awful for a while, but some fat perked them right up.
Stefansson, in his book, The Fat of the Land, describes how the Inuit ate primarily organ meats, and gave the lean muscle meat to their dogs. They considered vegetables to be unworthy of consumption by human beings. It turns out that in ketosis the body handles Vitamin C differently and needs much less from outside sources. Also, the fat of organ meats is a great source of vitamins from the B complex. Dr. Phinney recounts in one of his lectures that Stefansson retired to a small New England village and stayed keto to the end of his life, joking that it was good that he was the only one in the village who ate fat, because the local butcher gave it to him for free, instead of throwing it out. If I recall correctly, he died in his late eighties or early nineties in 1962.