your assumption is that subsidies and handouts help poor people. your assumption is just plain wrong. handouts are simply a way for the government to keep the poor poor. give them just enough to rely on so you get their vote. don't do shit else for them.
and you're buying into it. come on man.
There's a little more to it than just votes. The real core issue with welfare programs, and the Romans were really the ones who understood the value of this, is to keep the poor class at bay. Meaning, you give them just enough so they don't rise up and revolt. They were never designed as a safety net for the people, they were designed as a safety net for the rulers so the bottom doesn't drop out and get so pissed they rise up and take out those who are ruling.