I will also add that our entire Constitution came as a result of the Age of Enlightenment, including a range of ideas centered on reason as the primary source of authority and legitimacy, and came to advance ideals like liberty, progress, tolerance, fraternity, constitutional government, and separation of church and state. This Enlightenment was marked by an emphasis on the scientific method and reductionism along with increased questioning of religious orthodoxy—an attitude captured by the phrase Sapere aude, "Dare to know."
The Enlightenment also awakened a general interest in the various arts as mediums of expression in literature such as Daniel Defoe's Robinson Crusoe and baroque music exemplified by the works of Johann Sebastian Bach and George Frideric Handel gave way to the clarity, structure and technical brilliance of composers such as Wolfgang Amadeus Mozart and Franz Joseph Haydn. In painting, artists expressed realism through allegory and social criticism. Works that exemplified this trend were the court portraits of the Spaniard Francisco Goya and the English painter William Hogarth's street scenes of London.
Given that the Founding Fathers embraced the Age of Enlightenment so dearly, it stands to reason that they would want government to invest in the Arts as a means "to promote general welfare" of the new country.