The snobbishness of game culture never ceases to amuse me.
Video Gamer: "Pokemon is so childish!"
Normal person: "Video games are childish!"
I think Pet Battles are an interesting idea. I probably won't do a lot with this system, but it looks neat and I'm sure there will be people who find it fun.
It occupies an unique space, design-wise. In some ways, it's a solo PvP game, only without the crazy balance issues that would occur if Blizz made dueling a official sport. It does not depend on gear, so it's good for people who don't climb either the PvP or PvE grinds, while also not interfering with PvE or PvP.
It's a completely transient activity, so you can drop in and out. But it still leverages the multi-player and permanent aspect of WoW, as you get to play against other players.
It might be a possible sub-game for the people who want less twitch and more strategy, depending on how it's implemented. It would be easier to make the pet battle slower, or even turn-based, than it would be to change the regular game.
There are a significant number of people who can't or don't want to raid, or who don't want to be on the gear treadmill for PvE, and who aren't good enough for competitive PvP. These people need something to do, just as much as the raiders need raids. This is an option for those people.
I don't know if Pet Battles are the best option for this segment of the audience, but it ties into pet collecting, and is generally not as "hardcore" as PvE and PvP main games are. I think it's good for WoW to have these "softer" elements, and I would like to see Blizzard come up with more of them.
So what pet are you going to level and train? I'm going with my favorite White Kitten.
Also, Blizzard, make a [Faceless Minion] companion pet! You know you want to. We have a couple of die-hard pet collectors in my guild, and there is much sighing over the tiny Faceless Minions every time we go to Bastion of Twilight.