How do you know it wouldn't have the reverse effect, and make others think, "Oh, now I don't need to bother, Gate's has this..."?

I don't have the source handy, but I remember reading about when Gates and Buffet went to Germany with their giving pledge. One of the German billionaires they approach replied something to the effect of: "Why should I give money to support life-saving research or to feed the poor? Isn't that the job of the government? If I give the money on my own, then that removes the incentive for government to figure out how to take care of societies ills."

It seems unlikely that by giving $X we reduce the government's giving by even 1/4 $X. There's a huge amount of room for funding, and I don't think the apparent need the government sees decreases much as private charity increases.