Could more be done, of course! But the problem is that the government keeps requiring people to give them money so they can do the job, which leaves everyone else worse off since government never spends more efficiently than the private sector. I lose ~30% of my income immediately. Think what could be done with it if I were to allocate it instead of the government.
Not having property is not proper justification for violating the rights of others.
Edit: let me tack on that nobody benefits from impoverished citizens. They are a net drag as they need supporting either through charity or through social programs. It is in everyone's best interest to help end it, but of course you cannot violate the rights of others which means you cannot forcibly hold a mentally sick person against their will, for example. The problem with social programs is everyone shrugs off the duty because "the government is fixing it" while ignoring the whole of the moral hazard each and every new government program creates.