Charity vs. for-profit is a false dichotomy. A charity is a specific form of non-profit. In addition, there is the (relatively new) benefit corporation which, while technically for-profit, has explicit non-financial goals.

That said, nothing about being motivated by money means you can't have a purpose as well. That's why I was careful to draw a distinction between "solely" and "primarily". Making money while also improving the world is just enlightened self-interest.