Does 3 star fish only exist for desynthesis?

I just got my fisher to level 50 and looking forward to working towards catching every big fish, upgrading gear, and making some good gil, but I don't see any 3 star fish on the market, not even a name with a 0 being sold next to it. Can they not be sold? Or assuming they can I suppose those that caught one chose to desynthesize it instead? I did notice the things they desythesize into are very valuable.

EDIT: I'm mainly referring to Nepto Dragon. I just realized there are 3 star fish on the market. Just not Nepto Dragon.

Many threestar fish have little rewards in desynthesis and usually take awhile to fish up. Some of the 3* fish do have market value, Aetherlouse and Worm of Nym come to mind. However the majority of threestar fish are only interesting to catch for the big fish achievements available, which is something you can only get when you fish them for yourself. There are also a handful which desynth to swimgear and materials.

Nepto Dragon is a part of a fishing quest and has the untradable flag. So do a few others.

Oh, okay, thanks! Yeah I have that quest for Nepto Dragon which is what made me look it up on ffxivangler.com. I didn't know it was exclusive to the quest. I thought the quest was just to get one without realizing it was the only one due to being exclusive for quest.

There are a lot of fish that don't have a use in the game - including a large number of high level fish. Many don't even desynth into anything useful either!

But, that's part of being a Fisher. You do it because you want the fish and completion, less because you want the profit.