There's value given to a cause if someone important endorses it. Sure, a wealthy individual can write a check and cover the entire amount with ease, but why should he/she? You won't be rich for long if you hand out money every time you're asked. In the end, even the most generous wealthy individuals have to prioritize:

  -"I support X so much that I'll donate $100k."
  -"I like what Y is doing, I'll associate my name with it."
  -"I don't care for Z much/Z might be a scam, ignore them."

And sometimes the money will go toward a new house or a car. It's their money, and I assure you it's a lot harder to see from their perspective than you think.