There are several reasons why governments should not finance artists. First of all, artists should have to follow the same rules as the rest of the market. If there is a demand for their music or sculpture, then they will be rich. Secondly, politicians generally do not have good taste. They will waste public money on popular art or on their own preferences.
But the main reason why governments should minimize spending on the art worldis that there are more important areas like housing, roads, hospitals, and factories which need the money first.