Unfortunately the marshmallow test as a predictor of later success is debunked. It's part of the replication crisis in psychology. Half of the psychology we learned may be wrong. People just aren't that straightforward.
https://www.theatlantic.com/amp/article/576223
We also know people with high time preference/ delayed gratification are wealthier.
So now - what is controlling for parental wealth doing? It's removing this genetic component.
Social science is confounded by genetics all the time, once you start to look for it.