It largely is bragging rights, actually. Good PR is very valuable to a corp. And if the corp is running the charity it is also collecting donations to, then that's double the good PR. For example, if they're collecting donations for a charity that helps kids get involved in the arts, and they themselves run the charity, they can both say they raised a ton of money for charity and show the good work their charity has done.

This is good stuff, I want to stress. Charities are rarely for bad causes, though of course that can be slightly subjective and I encourage people to only support causes they believe in. But charity is being done, and the corp is not getting a tax write off, but rather good PR.