Attributed to the Eli Whitney Museum site by Wikipedia: "Whitney (who died in 1825) could not have foreseen the ways in which his invention would change society for the worse. The most significant of these was the growth of slavery. While it was true that the cotton gin reduced the labor of removing seeds, it did not reduce the need for slaves to grow and pick the cotton. In fact, the opposite occurred. Cotton growing became so profitable for the planters that it greatly increased their demand for both land and slave labor. In 1790 there were six slave states; in 1860 there were 15. From 1790 until Congress banned the importation of slaves from Africa in 1808, Southerners imported 80,000 Africans. By 1860 approximately one in three Southerners was a slave"
So whilst there are many inventions driven by capitalist investment that have had a far more benign or positive impact on society than your unfortunate choice of example, I think it's fair to say that profit-driven innovation by the already wealthy is far from certain to liberate people from the bonds that hold them in poverty even if it succeeds. I also think it's absurd to suggest that charitable giving can't foster innovation. Imagine if the local orphanage had given some smart, self-sufficient kids a good education focused on entrepreneurial values...
Imagine if Whitney had instead donated the capital he used to invent the cotton gin to the local orphanage.
I think it's an interesting commentary on the perception of capitalism that the world's richest view themselves as having been one-hit-wonders unlikely ever to eclipse their initial accomplishment with their own sweat and insight...
Instead, I'd prefer that these people follow in the steps of Gates himself, who has delved into asking the question of what the big problems are and how they're most effectively solved. His TED talk about power generation was incredibly inspiring, and assuming his wealth is $50B, he's not rich enough to self-fund it beyond the second stage.