This has been suggested many many times before, and every time it has been rejected. Like wolfwinx said, it would ruin the uniqueness and Res isn't made for breeding.
To expand on the economy thing, imagine if everyone started breeding Omni, Kioka, and Liyure, and the new CS pets when they came out. It would hardly be worth the credits to buy eggs anymore and there would be no more "retiring" since we could always breed the pets, devaluing them greatly. There are already a lot of them, and if everyone started breeding them, they would be worth literally nothing, selling for the low price of possibly even 1 tu per pet. Same with the seasonals, there's a reason they only come out once a year, it keeps them rare and valuable. Ebilias would be worth as much as a Gondra if you could breed, not exactly great for the economy. This would just make it really really easy to get yourself pets for practically free.
Not to mention, staff have said no enough times.