> We already have a system in place for every organisation to give part of their money for the public good: taxes.
Yes, but without any personal discretion or choice. For example, I personally think a woman's access to birth control and abortion is an essential right, but because this is by no means a popular viewpoint, I donate directly to charities that support my views.
Taxes aren't a way to support specific, desirable public goals, they only maintain the status quo. If your view had merit, Bill Gates would try to pay taxes to encourage redesign of condoms to improve Third World family planning outcomes (one of Gates' current projects). But Gates knows this won't work -- as far as a vocal minority of American are concerned, family planning is the work of the devil.
> As a democratic society, supposedly we already have mechanisms in place to decide how to spend this money for the public good.
You have a distorted idea of democracy. Democracy is not a centralized decision-making process in which various views are amalgamated into a single choice of action for all. Not to oversimplify, but democracy respects the rights of individuals and diverse groups to act in a way that doesn't interfere with any other group's similar rights. On this basis, private charity accurately represents democracy much better than centralized taxation does.