Efforts to promote private saving certainly have merit in theory, but the bald empirical fact for the United States is that the government has introduced a number of tax provisions to increase private saving over the past twenty years, and almost all of them have been correlated with a reduction in the overall rate of private saving.
These measures could have been effective at the margin, but they have not had a large enough effect to counter the general downward trend in private saving. As an added caution, from a standpoint of national saving, it makes no sense to introduce costly private saving incentives that then reduce government saving more than they raise private saving.