I don't see how this follows. Income is not evenly distributed across individuals, so tax isn't evenly distributed. So even if 50% of people donated 10-15%, that's no guarantee that it's the 50% of the high earners.

Also, philanthropy isn't a solution to systemic problems. It tends to focus dollars on the 'prettiest' problems -- it's not super attractive to donate to, e.g., portable toilet facilities. Aid programs ensure we're covering everything, including the ugly (or out of sight) problems.