Wrong. The original goal of IQ testing was to predict which students needed special care. It is still very useful (albeit expensive) metric for that.
I just mentioned wealth here just to demonstrate that just because something correlates and predicts something, it doesn’t make it interesting. We know how wealth is inherited, and how people of wealth are privileged and generally more successful (at least if we measure success the same way as IQ proponents do). We know the mechanics of how wealth works and we know it is more societal then psychological. I took wealth as an example here just to weather the possibility the IQ is correlated and has this predictive power because of similar mechanics, i.e. not descriptive of psychology, but society.
You are entirely correct, turns out I misremembered.
Wealth is definitely not inherited the same way as IQ, in that it doesn't show any regression to the mean. We also know that adopted children from a lower-IQ family will show an IQ between their birth and adoptive parents, which is again very different from wealth.
I do agree that IQ is not a perfect metric, but can you describe why you think IQ is more reflective of society than anything else?
Wealth is not a feature internal to an individual, it's something defined by a society/particular social structure and as such, it doesn't make a lot of sense to compare it to IQ (an individual difference variable measured by a test).