If you are just trying to promote success, then it stands to reason to reward success of the parents, incase some of those confounding factors are hiding actual fitness. After all, if the null hypothesis is true, you aren't losing anything by promoting some people over others, if they are all equality capable, anyway.
If you consider that there is no constant landscape, it's always changing and always an unknown, the best option is to try a plethora of different ideas, hoping some will succeed.
It's more like fighting a war in an unknown battlefield. If you play it just one way, you are more likely to lose than if you try many different strategies at once.
The ones that succeed will be self-sustaining, for as long as they are successful, anyway, and gain you enough ground to compensate for the strategies that didn't work.
If this wasn't true, nature would only have produced one single organism rather than a billion or more.
If we don't vary the amount of support people get, then we won't be able to take advantage of situations where more support (or less) would result in greater success.
And given that everything is constantly changing, there is no way to find a perfect level of opportunity to give to people.
So, a system that provides a varying level of support spread out against the population will do better nearly all of the time than one that provides an equal amount to everyone.
If you are going to go that route a better measure would be how much upwards mobility someones parents have demonstrated proportional to their starting point.
Of course that still suffers from a number of confounding factors (e.g. we don't know how much is down to luck)