Several elements of our musical practice have direct parallels in other arts of the same period. Ornamentation is one such element.
In the music we play, ornamentation is omnipresent, either explicitly indicated by the composer (such as is often the case in, for instance, Bach and much 18th-century French music), or implied by the performance practice of the period, which we infer from treatises, contemporary descriptions etc.
When not explicitly notated, nowadays we often tend to view ornamentation as an optional layer to be added to the fabric of the piece we play - a few ornaments should be added if the fabric is simple, and otherwise left out if the fabric is already rich enough. In many cases, and perhaps most cases, ornaments could actually be viewed as a key element, one which brings out the design features of a piece, highlights the beauty of the structure. It is not because ornaments need the structure around/behind it to 'hang on to', that they should be regarded in any way as less important, or less essential to the piece. In most cases, leaving out the ornaments compromises the exuberance of the whole, playing down other structural elements such as rhythm and harmony.
An interesting parallel can be drawn with the intricate art of embroidery, so much in vogue in the fashion of the wealthy European elite during the Baroque period. Here is one such example: a detail of a waistcoat front panel from c. 1760, with metal thread embroidery and sequins, applied to this beautiful blue silk: