After a long time not having a pet who would do anything, other than five me 3% powerpip, I think I finally understand pets and hatching. My myth-only basilisk has three abilities which are not epic or ultra-rare. Those three, which are rare or common, are all pet abilities, with nothing to do with battling. On the way to being ancient, I got all three of those. Worthless pet.
The fact that my pet trained those three has nothing to do with the future prospects of hatching. The abilities of this basilisk will always have the potential to create an awesome second generation. That pet may never be anything except a basilisk, in appearance, but, its the abilities which count, unless you're all about the appearance of the pet, and then there are only certain unique hybrids anyhow. I currently have three basilisks, one bred with a grimtooth (which I now got rid of), one bred with a Trojan horse, and one bred with another basilisk. Since I have acquired life mastery, I want a specific pet, with specific abilities. The card I get with the mythical basilisk is useless, because I have the bassy spell, and the colossal version of it beats the card in terms of damage. So, I will likely always have this bassy, unless I breed it with another pet that gives a card. I suspect that since I am myth, and this pet is myth-only, I am likely never going to get another pet, in appearance out of it.
How I really look at it is in terms of diluting the original pedigree of the first-gen pet. After that you never really know which abilities you are going to get, unless you train the pet up to epic and get a look at 4 abilities.