Hello, arandomplayer707! Although I do think perhaps some sort of implementation of breeding in Survival would be nice, making Eevee (and other rare Pokémon) common could really fracture their value. Though I'm a part of the group that thinks rare Pokémon should be a little more common than they are now (which is nearly nonexistent in the wild), the charm of actually having these Pokémon would surely take a hit. Perhaps limiting breeding of rare Pokémon to 1 or 2 eggs would be great. Also, this sort of topic should be posted in the Suggestions topic. Sorry for the long post, I have a habit of being a bit too wordy at times... XD
I would presume and hope the breeding would be like Pokeworld. Trading bred Pokemon would be impossible.