Keep in mind that what they put up on screen as a teaser lacks the polish of a finished product, and even being in raw form, it still looks good enough to serve its purpose; whet "our" appetites. I will reserve final judgment for the completed material when it is released, but so far what I’ve seen from the trailer is encouraging.
Also, I don’t see a problem with them constructing the ship on Earth. Space dock construction/launch scenes have been done ad nauseam in previous Trek films, but ground launches have not. If done right, to see a ship the size of a carrier lift off and head into space could be “spectacular”. Or it could be downright silly, depending on one’s point of view.