There is literally no nutrients that a vegan diet offers that you cannot get on an omnivorous diet easier. Vitamin D, just get sun light. Eat some fish and mushrooms or D fortified milk. Omega 3, if you're eating fish you're covered otherwise you should supplement(but you don't have to and getting fish to eat is easy). Magnesium, make sure you eat plants like kale. Zinc, almonds and meat. Glucose? Get some fruit or bread. Calcium, milk again. And vitamin D is what allows for your body to even use Calcium. That's why milk is a good source because it offers both in one drink along with fats to better transport the nutrients. Can you work around that on a vegan diet? Yes, but it's difficult. The only omega 3 options you have is from nuts which is ALA and not EPA/DHA which is what the brain uses. Or phytoplankton and that is a grey area for vegans. But even if you go that route it only offers 5% of omega 3s you would get from fish oil from fish or supplements.
Vitamin K is difficult to get on a vegan diet. I won't say b12, because most vegans use the carbs and sugars from fruits for energy.
The only thing against an omnivore diet health wise isn't even really against the diet it's more individualized. Like lactose intolerance or gluten intolerance or fructose intolerance (yes that is a thing and people who have it can die from eating fruit). Any way you slice it, an omnivore diet is better because of the variety it offers. Can you do well on vegan? Yes you can. Is it harder? Most likely, unless your genetic makeup does best with mostly plants for your carb sources. Is it perfect for everyone? No, some people function better with more fat in their diet like humans from west African cultures who have adapted to eating mostly fat. Or northern tribes men like Eskimos who are the same way. Fat is easier to get from animals. And there's just not always access to vegan fat sources all over the world. If a person has crohns disease they can't eat fruit meaning on a vegan diet there is no sugar source aside from breads which is fattening and makes you sleepy because of the neurotransmitters it stimulates for sleep. It's dinner food.