Why don't central banks just donate money to their poor citizens, rather than QE?
Most federal banks don't have the legal authority to do this, but the notion is definitely sometimes discussed, often under the informal name "helicoptering money". Former Fed Chairman Ben Bernanke discusses his thinking on the subject here, and some economists have called for this response to the current economic crisis. Rep. Maxine Waters has proposed a bill that would authorize the Fed to do roughly this idea.