We had a topic like this in the Pokémon chit-chat some time ago. Well, it goes against the foundation of Pocket Monster breeding. Imagine, the numerous breeding groups with countless Pocket Monsters crossbreeding? That's like... thousands of new Pocket Monsters. (And that does that require? Stats, movepool merge, abilities, sprites, etc) Also, egg moves are created by breeding different Pocket Monsters already. Lets look at Garchomp & Tyranitar, like your example. Chomp breeds with Tyranitar line to possibly obtain the following moves: Iron Head, Scary Face, and Thrash. So, say it did happen, instead of a new move, you're stuck with a new Pocket Monster. See? That's why it also goes against the backbone of Pokémon breeding. Unless the involvement of an item, but then we're running into the baby Pokémon nerve. And lets talk about Gartar for a second, what if that breeds with something? Think of all the things that might add / change.
Also, it'd be far too much of a hassle. (Sprites, etc) And I could only imagine more flames on Pokémon for lack of creativity. ("OMG WTF IS A FLYZARD?!1") Not only that, it'd probably spiral into pure confusion. We have a enough trouble figuring out the basics of babies, no? Oh! Speaking of, baby Pocket Monsters are kinda like crossbreeding. Rekhyt brought it up: "Theoretically, it can already be done by putting a Clefairy and a Clefable in the daycare. the Pokémon bred from them isn't either of them, instead, you get a Cleffa." So yeah.
It's a nice idea and all, but Azupichu? Overall, it'd simply be too much of confusion, hassle, and such a... drive off the breeding road. I can only see crossbreeding sending Pocket Monsters down a bad path. (The lines of evolution could branch out into so many alternatives it'd be... o_o yeah) I think the current breeding system is perfectly fine, and touching a nerve like crossbreeding could easily affect many factors. (such as sparking completely new things that could really mess up the metagame, from a competitive play perspective)
