I would make a different argument than Pinker's in favor of the notion that parenting matters.

Studies show that the normal range of parenting has a limited impact on outcomes. I will grant that.

The normal range of parenting styles is dominated by sub-optimal parenting, so studying the normal range tells you nothing about the impact of optimal parenting methods. Scientific research has provided evidenced-based parenting methods that are superior to those commonly practiced, but the technology transfer has mostly failed, in particular when it comes to getting most parents to practice the most effective methods. In fact, parents commonly chronically engage in actions known to be counterproductive.

So the issue of whether optimal parenting would have a bigger impact is mostly an open question.