This question is deeply misguided. "Meritocratic" usually indicates some rigid and static notion of merit, usually based on testing/scales/numbers games in mature and professionalized domains. So highest scores, most papers/patents, things like that. Even "highest customer satisfaction scores" is a meritocracy scale.
Being meritorious in this sense has very low correlation with being effective in most fields. "Merit" is entirely about individual qualities, "effectiveness" is about the quality of an individual in a given setting. Merit is neither necessary, nor sufficient for effectiveness. It is often a major source of ineffectiveness.
The clause "where luck, nepotism, etc. are minimized" shows where the question is going wrong.
Luck is good. Hire people who know how to get lucky. People with good radars, peripheral vision, daring and an opportunistic streak. They are rarely "meritorious" in any measurable way, but are highly effective. The meritorious types hate them, because their influence and rewards can seem disproportionate to their effort. These lucky, opportunistic types are often amateurish bumblers when evaluated purely on various scales of professional "merit."
They may even have NO personal qualities that contribute to their effectiveness: they may just happen to know one useful thing by accident. Would you give up a treasure-hunting expedition simply because the person who has the map is a happy-go-lucky drunk who happened to find it in a dumpster by accident while looking for food? Judge people by what they can do, not who they are. As Forrest Gump told Bubba's family, "stupid is, as stupid does."
Nepotism in its bald sense is random (hiring family members may be good/bad for effectiveness depending on the context and local culture, though in the long run it is usually bad due to regression to the mean), but interpreted more broadly as the role of personal relationships and trust, it is what makes the world go around.
Trust has little to do with merit; I'd hire a trusted friend over an unknown quantity with better test scores every time, unless I can develop that trust at sufficiently low cost. In fact trust usually conflicts with "merit" in the usual sense. People driven by a sense of their own merit are far more likely to create silos and optimize things to showcase their own skills regardless of what the business needs. If they scored 99/100 on Spelunking, but the business REALLY needs Skydiving, where they scored 70/100, they'll fight to keep the Spelunking department alive, and fight those who are willing to try and make the Skydiving department take off, even if they are lacking some skills.
The meritorious are often selfish, have a sense of entitlement, make all their decisions on a lazy auto-pilot and and rarely maneuver in response to reality. Though they are extremely "productive" in their chosen merit-badge earning numbers games, they usually lack the grit to survive through tough "needs to get done" efforts which test both their strengths and weaknesses.
Cliff Chang says athletics is different. Not quite. Perhaps that's true in individual, non-spectator sports like archery, but the moment you get to team sports with spectators, effectiveness and merit start to diverge. Ask any cricket, baseball or basketball fan, and they'll be happy to talk for hours about how the players who quietly go about doing what it takes to win games are rarely the more numbers-talented celebrities who are in it for personal glory, record-breaking and visible "merit" collection.
Merit can be a part of effectiveness when it manifests itself as true professionalism: a willingness to put a set of disciplinary values above one's own merit-increasing motives.
This includes recognizing that you may sometimes need to step back, and forgo merit-accumulating opportunities in order to let others do things that are more effective in a given context. This sort of professional behavior can only arise from a broader view of one's profession, which recognizes how it fits together with other professions and domains of value-adding activity that have not been professionalized as much. Merit-conscious people constantly pull rank, impose their point of view on every situation, and assert seniority and age. Worst of all, they label some things "beneath" them and have no sense of the dignity of labor.
True professionals never do any of those things. When they are required to lead by example, using their merit-winning skills they will. When they are required to do work "beneath them" and follow much younger, less senior bumbling amateurs simply because the situation demands it, they'll do that as well. Think Aragorn in LOTR.
Ultimately it comes down to John Boyd's distinction: in life you have to decide whether you want to be somebody or do something. The merit-seekers want to "be somebody" -- the award winner, the person with that title. The effective are "do something" people.
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