I noticed that these are sellable and for a decent price. Is there a reason to keep them? Do they have any value outside of just completing Shinwa's quests?

No, they can't really be used for anything except completing Shinwa's quests. It could be helpful for someone to buy the pieces if they forgot to start Shinwa's quest first and had already completed all of their Wizard's quests, for example, and then Shinwa asks them to complete a Wizard quest to get her bracelet piece. Since they would be unable to complete the quest otherwise, since they have no available Wizard quests for the day, they might just purchase the bracelet piece to still be able to complete Shinwa.

Or some people might want them for a gallery or pet TC or something like that, just to collect.

Gotcha, thank you! ^^