Well first of all vitamins do NOT work without mineral cofactors. That means vitamins need minerals to properly function. Having said that, some diseases are due to deficiencies but NOT all.
For example, it has been discovered recently that high serum uric acid over a length of time causes several metabolic diseases, including the most common such as type 2 diabetes and high blood pressure, both known killers.
Within the next year or so this information will change healthcare as we now know it. Uric acid level will become the most important part of the blood test, not cholesterol, not A1C, virtually none of these tests/ results will hold a candle to knowing and controlling uric acid in the body. Once uric acid is under control, all 100 metabolic diseases will disappear.
On a final note chronic high blood pressure is controlled by the kidneys. Even if you manage to finally lower and control your uric acid level the kidneys have the final say on weather your blood pressure comes down or not, and that depends on the amount of damage done to the kidneys.