The Medicis used the artists for their own purpose, because they wanted to make their family more powerful, richer and more famous. Therefore, they looked out for the best painters, artists, architects, scientists, geologists and writers in order to take benefit of their work. They liked also the positive and soft image they got from the prestigious work of their patronized artists. On the other side, as today and in recent history (3rd Reich), many artists like to be linked to power, and are attracted by powerful people/names. So, the relationship between artist and the Medicis was probably not a one way street. Without the financial help of powerful people, like the Medicis, many big achievements would not get real.
The merit of the Medicis is their support to such a wide variety of art and science and their good taste in selecting those artists/scientists we still view today as the best of their time. For this, they deserve their fame in history.