I really disagree with this. Consider a simple counter-example. Workers in the Bay Area are substantially more productive than the American average.
One simple way to use capital to increase GDP is to build more housing and infrastructure in places like the Bay Area. Even if the population doesn't grow, that housing stock will allow future workers to move from West Virginia to San Francisco.
By shifting future workers from low-productivity job markets to high-productivity job markets, we can substantially increase total economic. Even with the same population and the same technology base. The only constraint is the tight housing supply in places like the Bay Area. But we know how to build more housing, all it takes is a willing political system and capital investment.