I have not found promotions into management to happen among the most competent. Companies lean toward keeping good employees in their position, and those with less competence get moved around, many times into management positions. In my experience I've come to believe that management is very difficult because most people don't get it. Out of all the companies I've worked for and all the management I've worked under or with, I'd say less than 10% are competent, and and the best was female.
Why was she best? Because she was good at organizing, good at following up on performance reviews, good at letting her team do what they were best at, and good at making decisions because her communication with her team allowed her a good pulse of what was going on. A large portion of male managers I've worked with want to be too hands on, and shirk some of the most basic organization and coordination that is needed to run a team. Lets face it, the bulk of a manager's responsibilities are secretarial tasks -- calendaring, organizing, scheduling, basically keeping their team on task. Some people get that, some people don't.
It is ideal to have a manager who was competent in a skills position at one point in their career, and work their way up as does a manager of a loading dock, but it isn't a requirement. For example in contrast to most other countries, many Chinese government officials have engineering backgrounds, and they "get" technology, and thus they seem to make much more intelligent decisions for their countries in many areas, e.g. manufacturing. In contrast, U.S. politicians are all lawyers, who are adept only at diverting and twisting issues for their own agenda rather than a pure sense of "good" and "not as good".
So background is important, but based on the high failure rate of managers I've seen in my decades of work experience, I'd just like someone who is a competent organizer and decision maker. Asking for someone who is good at that and who truly understands the jobs and skills of those underneath them is nearly impossible to find. That is largely because managers are hired by "Directors"--career management straight out of school, who don't have a clue how the world works above or below them... and Executives are skilled at sales. No one really gets it, and thus my opinion of corporate organization is very poor, so the most competent skilled workers have no desire to get "promoted" into a position largely occupied by incompetents.