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.
The thing is, there are always explanations.
Given that Scotty was throwing a fit and apparently walks off, maybe Chekov is the first person Kirk sees around in the moment and figures, "What the hell." Could be he expected Scotty to eventually come back after everyone cooled down, too.
The entire "give everyone something to do" thing bothers me, though, because it does lead to contrived situations like this.
Not to make too big a comparison (because of big gaps in their experience), but Miles O'Brien on DS9 wasn't an officer or even Starfleet, but he was chief engineer on the space station.