They obviously have zero interest in creating a competitive environment, and even if they did care they have no one working for them that could facilitate the necessary changes to make it work.
Obviously? I don't think it's that obvious. In fact, I don't think it's even accurate to say. The way they're doing balance now seems to take a page out of the book of other competitive games (league) where balance changes happen frequently and in small numbers. This stands in stark contrast to how blizzard has approached balance in the past, and could easily be them making an attempt to make their game competitive. Then you have their "end of year" 2014 post, with this section in it:
The new War Games skirmishes feature allows anyone to run an online tournament, and we’re excited to see even more community-run tournaments in 2015. We’ll of course be running tournaments with our eSports partners as well, and will release details as those plans are finalized. As you saw at the Arena World Championship, we’ve come up with an improved UI to help viewers better follow the action, but we’ve been working on a complete overhaul for next year—with the goal of making it widely available for use in player-run tournaments, partner tournaments, and online casting. We hope to be able to share more soon.
Which is a massive deviation from the bullshit stance they've taken in past years of "we don't encourage it as an esport, people want it to be but we won't let it". To say they've obviously got zero interest in making WoW competitive is seriously overreaching IMO. Looks to me more like they actually somewhat want it to be but just suck at it really badly, as would be expected.