How do obligate carnivores not have nutrient deficiencies?

To add to Bryans answer there are a few other issues.

mainly pickiness and brains.

Human can handle an all animal diet surprisingly well, look at the modern Mongolian nomad diet, which is exclusively animal based. One problem we see in modern humans in industrialized nations is they often avoid eating organ meats, eating only muscle tissue "meat" can easily lead to a nutrient deficiencies. Ask yourself when is the last time you sat down to a liver or kidney dinner. many vitamins are almost exclusively found in organ meats and not muscle tissue. So many times when people from first world countries end up on an all meat diet they end up with deficiencies because they are not eating the vitamin rich portions of the animal.

The other problem is humans have very big brains, and brains can't burn fat. They can only burn carbohydrates or protein. you may already see the problem, animal tissue is rather poor in carbohydrates. But, you say, they have lots of protein, which is true, but humans along with many animals do not metabolize proteins well, doing so on a large scale leads to ketone and other toxic byproducts. Human brains demand so many calories that they burn thorough what little carbohydrates animal tissue have, very quickly forcing ketosis. So humans must burn far more protein than most other animals on a all animal diet even when lipids are available because carbohydrates are lacking.

Carnivores also have adaptations to better deal with ketones, they still produce a lot of ketones but have better methods for managing them, mostly better ways to excrete them. Most apes only eat small amounts of meat and rarely lack carbohydrates in their diet, have not needed this adaptation. This is true for most of human history and the exceptions are very noticeable. The Mongolians I mentioned earlier also eat a lot of milk and cheese which contain a decent amount of carbohydrates.