On a more technical point, the duo has potential to fare well in the competitive scene, having both good zoning tools with both egg types while at the same type being able to negate zoning with Wonderwing, and having average mobility. Nothing is certain right now, obviously, but the chatacter shows promise.
I do agree that the duo has a lot of potential - but I stand by my previous point that B-K's frame data will be the main factor in determining whether they're viable competitively or not. Of course, that's not going to affect much amongst posters here (most of us are casuals I bet), but that does impact matchups and what to expect when playing online or whatever. I also stand by that B-K can do pretty well vs.

,

, and

, but struggle vs.

,

and

- even casually.
For example, we don't know if Up-B has a hitbox yet. If not, good! If it does, well, B-K's now open to being Countered under the ledge like so many others. Also, related to that, if Kazooie can be hurt then that's a major problem too.
That said, I think we can infer some positives and negatives from just the trailer (Note: This is far from a final assessment, but an inference. Can turn out completely wrong by the time B-K releases):
+ Great horizontal jumps: Aids with approaches and ensures one can be flexible with Eggs / Wonderwing.
+ Decently quick attacks: Allows B-K to mix-up and keep up the offense up close. Also allows B-K to keep opponents guessing, which I think will be key to B-K's game, both casually and competively.
+ Good reach on the ground: Allows B-K to space tilts, smashes etc. pretty well. Also helps to pressure shields.
+ / -: (This is crucial - does B-K have little start-up / endlag, or not? We haven't seen most moves, so it's difficult to tell.)
- Bad / Mediocre vertical jumps: Could be a problem in Battlefield stages mainly, might result in B-K having trouble / overcommiting with follow ups sometimes.
- Likely medium to heavy weight, but also possibly floaty. Makes B-K's possibly vurnerable to combos and tech-chases.
- The eggs don't appear to have that much priority (normal Eggs), or can be grabbed (Grenade). Hinders spammability, and can turn out nasty if lets say Inkling throws her bomb at B-K (the bomb out-prioritizes almost every other projectile in the game though, extreme example).