We should be able to choose if we want a pet's spell cards to be included in our decks. I'll give you a perfect example. The Coldfire Dragon, at Mega, gives you 3 Eirikur Axebreaker spells. On my fire wizard, I'd rather cast a Fire Dragon, which can be boosted by colossal, for the same 7 pips. Eirikur Axebreaker isn't a bad spell, but I just wouldn't normally use it.
How I propose this works is simple. If a pet gives you a spell card during it's aging process (not pet talents because you can either train them out if you don't want them or train them in if you do), there should be a box next to the picture of the pet, in the pet screen, that you can check. When you check it, the pet includes the card(s) in your spell deck. If left unchecked, no card gets added. This option should ONLY be available if the pet you have equipped gets cards from the aging process.