You make a huge unspoken assumptions that people actually care about charities getting their stated work done. There's very little evidence for it, and plenty of evidence against it. As far as we know people donate time and money to charities to signal their moral character to others, and to receive pleasant feelings of contributing in return.

So you'd be right, if your basic assumption wasn't so completely mistaken. To be honest this assumption is extremely common, so it's not just your mistake, but it doesn't make it any less false.