This kind of "meritocracy" is more like if we held an arm-wrestling tournament, declared the victor to be our new feudal lord, the next 6 runners up to be knights, and everyone else to be peasants. Our position in this new society was based on "merit", but that can't necessarily justify the difference between nobles and serfs.
We could even re-run the tournament every year. We could make sure no child gets extra time in the weight-room because of her noble parents. We could decide that arm-wrestling is stupid and brutish and so, in a glorious revolution, switch to speed chess. None of it would address the question of justice.