Very few people eat so healthfully that they get the ideal amount of every vitamin and mineral needed in optimal amounts. Therefore for most people, using a safe, well-designed multivitamin can be helpful. Even then, no supplement or multivitamin can take the place of a Nutritarian diet with its full spectrum of both discovered and undiscovered nutrients. However, even when eating a nutrient-dense, plant-rich diet and minimizing animal products for longevity benefits, you run into the issue of being sub-optimal in certain nutrients that are more readily found in animal products.
But taking in more animal products would not be the answer, as then you run the risk of too much animal protein, animal fats, heme iron and other animal food-based pollutants.
When deciding on a supplement, it is important to note that most multivitamins contain ingredients that can be harmful, and even cause more harm than good. Certain ingredients, like copper, beta-carotene, vitamin A and vitamin E, have been shown in studies to have health-degrading (even cancer-promoting) side effects, whereas other ingredients, like iodine, zinc, vitamin B12, vitamin K2 and vitamin D3, are important to supplement because they can be difficult to obtain in optimal levels through plant foods. Taking a properly designed multivitamin and mineral supplement can be an important contributor to great health.
Remember, all scientific studies testing multivitamins are almost worthless because they are studying an intervention with too many variables, both potentially positive and negative. Testing multivitamins containing Vitamin A and folic acid is invariably going to negate any potential positive from helpful components such as B12, zinc and Vitamin D, because folic acid and Vitamin A can distort normal cellular biochemistry.