Historically, I'm not really seeing meritocracy as "meritocracy hopes to fix injustice in the inequality of our world" - instead, it's an observation if you put incompetent people in positions of power, then everyone suffers; and you'd do best to fill all the important roles with people who are actually good at it.
The point of meritocracy is not about the benefit to a capable person who gets to be in a good position; it's about the benefit to the system from a capable person being in that position. This effect is what makes meritocracies more efficient and competitive than other societies.
And there's really no reason to expect that meritocracy would fix unequal distribution of wealth; as equality of outcome is fundamentally incompatible with equality of opportunity; and all kinds of "merit" characteristics (conscientiousness, impulse control and similar personality traits, intelligence, educational achievement, physical traits, propensity to addiction, etc, etc) are all quite heritable; no matter how much of that heritability is nature vs nurture, the "merit" of children inevitably will be highly correlated with the "merit" of their parents - so we should expect a meritocracy to have some "sorting effect" across generations as described in the original article.
Meritocracy will allow for some class mobility anyway, as a significant part of "merit" traits is also essentially random, however, a significant part of them is not. An 'meritocracy-upper-class' kid is not necessarily more qualified than a 'meritocracy-lower-class' kid for some position, so it needs to be evaluated and in a true meritocracy some (!) of the lower class kids would raise up, but statistics indicates that most of them would not.