This question has been addressed before, but whose answer is worth repeating. Sakurai changed many things in Brawl from the basic Melee engine, and added many things also. One change was making air dodges non-directional. Some reasons for this change off the top of my head:
Sakurai wanted to allow players to do moves after a dodge and directional dodging would've made certain aerial techniques overpowered (think multiple jumps). This also drastically reduced accidental self-suicides, since players can not air-dodge off the stage and still recover after an off-stage air-dodge.
Sakurai may have also been thinking about the speed of the game, and lessening its complexity. Since the intended purpose of the air-dodge is to protect oneself from attack, why do players need to input a direction? This also relieves some of the stress on the WiFi since the game can read less variables.
Did this change take out wavedashing as we know it? Yes. But was that Sakurai's specific target? Many of us believe it was only a secondary purpose, since others have stated more direct methods of removing wavedashing, like restricting air-dodging opportunities, preventing any sliding, etc.
If you were to elecit my opinion, Sakurai viewed wavedashing nearly the same way any seasoned tournament veteran does: a simple manipulation of the game's physics engine that did not reduce competitive play to a showcase of superior wavedashing skills (as is often the case with fighting game exploits, i.e. David Serlin's famous anecdote about super-canceling in one of those Street Fighter games), but thankfully add layers of depth and variety to the game. I think there is evidence to this theory in the fact that in the PAL version of Melee, many individual character moves, and even core character properties like weight, were adjusted, or "corrected" for balance, but wavedashing remained.
As is the way with most topics about wavedashing, the more "green" players come in and wail and whine about pros winning "just because they can wavedash", having never seen great players compete, or if they have, not fully understanding the complexities and nuances of situations that occur in top caliber matches. "Pros win + Pros wavedash = wavedashing wins" is flawed logic.
I'd like to see the equation like this: Players are like craftsmen. techniques like l-canceling, wavedashing, dash-dancing, are like tools. No matter the quantity or quality of tools the craftsman uses, the knowledge and skill of the craftsman is the same, with or without any individual device in his arsenal.
Wavedashing is not an overpowered technique, like some percieve it. It's use requires many complex decisions, like length, direction, and timing, and is best utilized by those with great understanding of relative character speed, attack ranges, and stage spacing. Often, it is best not to wavedash at all, unlike l-canceling. With l-canceling, there are no decision. You do it every time. (I'm glad Sakurai made l-canceling easier, since it is such an essential mechanic of the game). Some character don't even benefit much from wavedashing, like Link, Jigglypuff, and Captain Falcon.
That said, I hope we all have come to terms that though Brawl builds on Melee, and will share a great number of similarities with it, there are noted differences, and there will be more. Sakurai streamlined returning mechanincs like air-dodging and l-canceling, simplifying their implementaion and use (cleaning house, so to speak), so that he could add more moves and systems to create an even more rich and diverse game than Melee. I just hope that, when the new Brawl techniques are discovered, eveyone can view them with an intellectually mannered approach and not prematurely doom the future of what could be a game for the ages.