There are a few big issues with the average consumer eating fortified foods regularly. Your body does not absorb individual nutrients added to foods in the same way that it absorbs nutrients that naturally occur in whole foods, consumed alongside all kinds of other complementary nutrients.
A simple example is skim milk that is fortified with vitamin A and D. The milk has been processed to remove the fat, but A and D are fat-soluble vitamins. So if you eat them without a fat source, you may not benefit in the same way or to the same degree.
Furthermore, most food companies are using a synthetic version of the micronutrients, which your body may process differently than the natural, food-based version.
Finally, companies often add vitamins into these foods at incredibly high levels (up to 100% of the recommended daily amount into one serving of food). Since most people don’t have severe deficiencies, eating a lot of foods that are enriched or fortified may cause you to exceed the recommended daily intake by a long shot.
In severe (although rare) cases, this can lead to toxicity overload. Some individuals have trouble breaking down folic acid, and eating enriched cereals (and derivatives) could cause blood concentrations to increase to a level that can consequently decrease immunity or mask a vitamin B12 deficiency.