Motifs are learned to craft gear in a certain appearance using matching style stones or to use the Outfit System to create an outfit of that appearance for gold. They also allow players to do Master Writs, which require crafting specific gear in certain motifs.

The vast majority of motifs and their pages are available for free in game by doing in game activities and events or on sale for gold in guild stores. Thus the high crown store cost is an incentive to earn the motifs in game or else pay for the convenience of getting them in the Crown Store. The exception are the few Crown exclusive motifs (which are never used in writs). Those are Tsaesci, Grim Harlequin, and Stahlrim frostcaster.

Edited to add: its almost always cheaper to buy the non-exclusive motifs with in game gold. Additionally, the Anniversary Event in April features motifs pages as a common rewards. So if you need to fill out motifs cheaply, its worth saving your gold until then as prices usually drop.

There are three motifs that are crown store exclusive - Grim Harlequin, Stahlrim Frostcaster, and Tsaeci. If you absolutely love one of those for its appearance, then it might be worth spending crowns on. These could be gotten for in game gold via crown store gifting, but it's a bit more involved than buying other motifs from guild traders.