Gates has the money to do both, and more. It’s just sometimes better to let others do it instead— having your own space company means worrying about competition, contracts, and potential profitability. Meanwhile if he wanted, he could hitch a ride on any of their rockets with no effort.
Musk and Bezos also have the money to do both, but they merely elect not to. Perhaps in the future they will, like Gates, begin funneling more of their effort and wealth into altruism to improve their reputations.