Public debt reduction makes more funds available for investment and puts downward pressure on the cost of capital. Alternatively, higher saving can come from the private sector deciding to consume less and save more, which also channels more funds into investment and puts downward pressure on capital costs. From a macroeconomic point of view, it doesn't much matter whether the saving is public or private. The choice is pragmatic. We have tried a lot of different incentives in the last decade or two without any visible effect.
Private saving remains low.
Hence, paying down public debt has the obvious merit of being something we know how to do. Increasing national saving isn't a guarantee of higher growth in the future, nor is it the only prerequisite for a more productive economy. The increased saving has to be used well. It should be combined with a steady stream of innovations ready to be turned into products and processes, successful investment in human capital that results in upgrading workforce skills, and a widespread managerial focus on continuous productivity improvement. That all sounds like what is happening in the U.S. economy right now, so one way to contribute to a higher GDP over coming decades may be to figure out what we are all doing so right in the current U.S. economy and keep doing it.