If only the best fighters can be knights but those raised in wealth have a vast advantage but any peasant outliers can become one it is more meritocratic than one which only allows those of noble birth but selects from canidates within. The fact the nobles compete is the only thing which gives a scintilla of meritocracy.
A system of commissions for officers based entirely on wealth would ironically be less meritocratic than the nobles only pool because it doesn't factor merit in at all.
The adhectives eglataran and meritocratic are technically two separate aspects. Although they are synergistic in that the aspects are stronger together than apart. Equal opportunity of resources would be more meritocratic than a "pure" meritocracy and more meritocracy undermines "gatekeepers" which may emerge among eglatarans where merit isn't what determines advancement.
Someone with talent from an average background is going to be "out-merited" by someone with average talent from a privileged background - because the privileged person will have the resources to develop their skill, while the other person won't.
In fact not only will they not have the resources, they'll have extra costs - in the form of forced time spent working away from music to pay the bills, college debt, and so on. And of course limited access to physical and social benefits - good instruments, lessons, practice facilities, and ultimately choice of college and the resulting class network.
Apart from the obvious financial implications, those distractions will saddle the victim with a huge extra cognitive load.
A lot of people will be crushed by it, no matter how talented they are.
And the merit here is producing great music; working hard is not a merit. It can command respect, though, and indicate a future growth potential.
A child is never wealthy; the child's family may be. Being born into a wealthy family is a privilege. I child who doesn't waste that privilege, and makes the best of the somehow elevated starting position, deserves as much respect as a hard-working child that achieves impressive results starting from a worse position. It's pretty easy to just coast and achieve nothing if your parents already give you everything.
The usual textboook definition of merit in the context of a meritocracy is "talent, effort, and achievement".
> A child is never wealthy;
That's just somewhat true in our particular flavor of society, and even there children may be wealthy independently of their caretakers.
In a meritocracy where merit is essentially equivalent to wealth or currency, a child may very well be considered wealthy just on its own.
A pure meritocracy doesn't even guarantee that a child could be wealthy without having talent. As soon as someone with wealth but without merit is able to obtain economic goods (such as the highest quality training and equipment) that are not obtainable by those with merit, whatever system you have ceases to be a pure meritocracy.
It's not a meritocracy.