Is there a reason (poor stats/skills?) that people don't sell GP3 Gryphons, Cockatrices, Pumas, Throdamas, and Lykos?

On the market, I only ever see Unicorns and Symurghs, with the occasional rare Dragon and Roc.

Unicorns and Symurghs are fairly popular pets. Because they're popular, people are more likely to breed ones with good genes and end up with GP3 pets with good stats for fairly low prices.

Dragons and Rocs are also fairly popular because of their elemental attacks (Fire/Napalm Strike and Lightning Strike, respectively) but I guess not as popular as unicorns and symurghs.

Lykos are fairly new and all of the original Lykos came from a Christmas event last year, where they hatched from egg items. Those egg Lykos had average stats, and as they were bred, the bad stats got bred out but no good stats were added. Also, because they're only about 6 months old, there probably haven't been many GP3 Lykos breeders.

(GP3 pets have very specific requirements, which a lot of Lykos do not meet. Timain has a Newbie Guide that talks about GP pets: http://beastkeeper.com/thread/5218 )

Throdamas, like Lykos, are available in the wild only from the Battlefield. Symurgh are also available from this same place, but they're more popular and more likely to be bred for good genes. Throdamas aren't really popular as far as I can tell, and because they're so unpopular, there are fewer to breed with, a narrower gene pool, and overall poorer genes.

While Cockatrices make decent battle pets because of their species abilities, they too aren't terribly popular and are thus not common as GP3.

Pumas I don't know about, probably because more people care about colors for Pumas now that Puma deviants exist and not so much about GP3 stats.

TL;DR: Popularity of species and size of gene pools.