Good question! I think that can play out both ways, ultimately based on how wealthy the parents are. If money is no object, play the prestige game. If you are middle class and know the rules of the game, maximize value.
For example, I am acquainted with parents who are teachers at a prestigious private school. Their child attended said school because of subsidized tuition, and then attended college in an honors program at a state university in the middle of the country. He was paid to attend! The parents are fully abreast of all the studies on the effects of education, both being teachers and being in the middle of the college admissions frenzy that goes on in these schools. So they know how the game works, and they are playing it to the max for value.
On the other hand, at this school are children from generational wealth who play obscure sports from an early age to give them an edge in admissions. The children never need to actually earn a living, and the target school admission is seen as a defense of a family legacy and bragging rights for the parents - pure prestige.
> children from generational wealth who play obscure sports from an early age to give them an edge in admissions
This is a really good summary. The end result is a permanent, non-transferable, protection with strong resistance to “inflation”.
> they do have some inside perspective compared to the population at large.
Would that advantage manifest as playing into the system - looking for opportunities for signaling? Or discounting - finding good education with less signaling value.