- The budget of a democratic nation isn't under direct control of its constituents, so average selfishness of the citizens has nothing to do with it.
- A democratic nation has lots of interests jockeying for the budget, and can easily swallow arbitrary amounts of money.
- Almost all of that money is spent on improving the things for that nation, so a nation state is not the best organization to task with solving a global/international problem.
Most importantly though, the more diffused the money, the less effective it is. Coordinating people costs a lot (think of how much charities spend on advertising!). With his fortune, Gates can just drop $60M on some promising anti-malaria activity; in the alternative reality d-d/you are proposing, it's unlikely that 600 of his employees would suddenly coordinate to drop their $100k on that operation; most likely, no money would be donated at all.
So the argument essentially boils down to focus. Much like with distractions and personal productivity, both the market and a government budget can absorb arbitrary amounts of diffuse money with little of value to show for it; it takes focused, bulk money under control of a person to move the needle on some issue.