Just a thought...we have to get used to the warp 10 scale no longer being valid in this universe...they are taking the element from Star Wars that makes storytelling easier...almost instantaneous supra light travel, in this case a transwarp like speed.
I don't necessarily have a problem with transwarp beaming, especially how it was described in the last movie. There have been science fiction stories in literature for years about long distance near-instantaneous travel, so it's not unprecedented.
ST has always played fast and loose with ranks. Again this is not really a big issue to me. Hardly indicative of bad script writing.
Perhaps not 'bad' but childish. Kirk's promotion was childish in its lack of realism for all the reasons spoken by Pike in this film. Chekov's promotion was childish in its realism. It isn't just about that fact that Chekov has just been placed in charge of about a dozen people who outrank him - it was a hamfisted way of giving him something to do. They could have done something similar without actually making him the chief.
Transwarping is childish. It doesn't pay any attention to their own established laws of physics. I'm not saying that the distance is the issue - its the timing and the method of actually knowing where you are going to end up that make no sense.
Trek has always been a bit silly but I just feel they are pushing the envelope too far. Re-watch early TOS in the light of the fact that it was made in the sixties. The science feels so much more sensible and grounded.