This is a complicated answer; belief/understanding morphs greatly over time and is not uniform in any instance since Greco Roman times. Scholars note the Byzantine period (particularly for its "bright" use of gold to signify for the ubiquity and omnipresence of God, later described as garish by artists/art historians such as Leon Battista Alberti (1404-1472)) as a hard/soft break/shift (depending on who you ask) from Greco Roman ideas about form and color. So in short, debate about the use of color as you're asking occurred in ancient Greco Roman times and came about fiercely during the Renaissance. Bright and full-spectrum color palettes were always associated with "immaturity."

I can point you to a few concepts that Patricia L. Rielly expands on greatly in her article, "The Taming of the Blue" which you can find in the anthology Expanding Discourse: Art and Feminism. The question you're asking about not only deals with the question of bright/full-spectrum vs muted color palettes but rather an age old debate about disegno and colore. This takes a bit of a gendered conversation, which I will minimize, but one may perhaps liken disegno (male), or design/form, to the "ideal" in platonic terms and colore (female), color, to "matter." Disegno is the blueprint and colore fills out the blueprint. Since Greco Roman times disegno was almost always given precedence over colore because an "idea" is the foundation upon which "matter" is built. It behooved the artist to master disegno rather than colore because mastery over colore without full mastery over disegno is "deceptive." It was believed that color could be used to fool/seduce the viewer into believing that a work of art was "good" when in fact color was being used to mask the flaws in the "design" of the artist. Therefore, to really make disegno pop, artists carefully tip-toed around colore opting for a more muted color palette. Nevertheless, dissenters in both Greco Roman times and during the Renaissance placed equal or more value on colore, which Rielly mentions and sources as does the scholar Ian Kennedy. Kennedy states that Philostratus (c. 170-250 CE) in Imagines argued against the classical tradition and that color was an essential life giving form. Kennedy postulates (with the formal analysis of art) that Philostraratus' opinion perhaps influenced 16th century Venetians, who had often argued along similar lines, that colore was the means by which disegno was actualized. The Venetian voice was heard on some level by others in the Italian Peninsula. Michelangelo was always considered the greatest artist because his mastery over form was considered greatest by Italian writers of that era. However, even Giorgio Vasari (1511-1574) had acknowledged that Titian's mastery over colore made at least one work greater than Michelangelo's because Titian had mastered both form and color in a way no other artist had ever achieved. It is a bit ironic because Titian's palette was bright, as you'd say. In any case, his attention to form solidified him as an artist.

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SO TLDR: Muted palettes were always favored in western culture because it allowed the form of the work to speak for itself. Bright colors were always believed to "fool," "entice," "deceive."