I can't speak for theatre or music. But for painting, in the West, the central debate over the legitimacy of painting occurred in its transition from a mechanical craft to a member of the Liberal Arts (essentially what it is believed to be today), a process that began during the Renaissance and more or less culminated in the rise of the European art academies in the 16th and 17th centuries. In short, the idea was that painting considered as craft was unintellectual and subservient to external demands, whereas painting understood as a Liberal Art was theoretical, intellectual, and free. In essence, Renaissance artists and theorists wished to see painting join the seven Liberal Arts of late antiquity (Arithmetic, Geometry, Astronomy, Music, Grammar, Rhetoric, Logic). This resulted in a new emphasis on the teachable, theoretical, "scientific" aspects of painting, and that painting be grounded on empirical, theoretical, and scientific branches of learning, like optics and anatomy. The writings of Leon Battista Alberti are key here, as is the "invention" of perspective as a quasi-scientific technique. At the same time, arguments for the equivalents of painting and poetry, relying on Horace's "ut picture poesis" flourish from this period and remain central to academic art practice right up to the rise of Modernism. This is a response to the rising status of poetry prior to the Renaissance.

This "vetting" process, to borrow your term, was a way of arguing that painting was a vehicle for the free play of the imagination and that painters could therefore be considered true creators, in some manner divine (Michelangelo was called this) or divinely inspired. Thinkers like Marsilio Ficino returned to Plato's notion of inspiration to argue that poets, musicians and painters could be seized by a divine madness. This is the origin of modern artistic identity (signing one's works becomes more widespread in this period) and of concepts like artistic genius. It also represents the origins of the art/craft or free/applied art divide; the European art academies cast themselves as teachers and defenders of painting as a liberal art against the guilds, whom they saw as lowly, unintellectual producers of mere mechanical craft or applied art.

Anthony Blunt, Artistic Theory in Italy, 1450-1600, is good place to begin.