The reputational aspect is definitely a big part of it - they want to be seen and remembered a certain way. Bill Gates is a good example, but he blew all that up by raping children (maybe). Before the Gates Foundation, he was viewed by the public as a typical evil miserly cutthroat businessman who was also a weird nerd. Gates Foundation & making sure everyone knew about it did a lot to sway public opinion.

And the actual people at the Gates Foundation did great work - they helped to control and eradicate deadly diseases in the global South. But it isn’t like Bill was doing that work, he was just allowing someone to cut the checks.