Well he didn't get it because of any empirical evidence that he was a great captain because he'd basically never captained before.
There is a long held theory that bowlers don't make good captains because they can't be objective about their bowling and they get too hemmed up in their own bowling to make clear decisions about field placements, bowling changes, tactics etc. etc. Such a theory informs why Broad and Anderson and to a lesser extent Stokes did not get much consideration at the time for the job. And in terms of constants in the batting order you were only left with Cook, the incumbent, and Root. So Root got the job.
Unfortunately for Root, unlike say Mike Brearley who had 5 years of doing nothing much special at Middlesex as captain before 1976 where he won the County Championship and got the England job, he's having to learn on the fly in the most difficult arena of them all. There's not much a captain can do about rubbish calls for 2nd runs and dropped catches other than tell his players not to do these things.