Christ obviously had quite a lot to say on this subject. But, as you skim through the above verses, notice what words do not appear: "government," "State," "policy," "law," "tax." He is not merely telling us to submit passively to some third-party administrator who will see to it that all of the tunics are evenly distributed, and all of the banquets diversely attended, and that a certain mandated portion is given to the beggars and the borrowers and the needy. Christ never established or suggests or endorses any State-sponsored system by which these things will be achieved. He makes it much simpler for us. He puts the onus not on politicians or bureaucrats but on someone else entirely: you.
I can't help but note that, so often, the Christians who advocate higher taxes and higher welfare spending are also the Christians who will not be affected by it. They want "the rich" to help the poor, and they imagine that their personal responsibility to give to the poor has been alleviated this way. It hasn't. Regardless of taxes, if you're keeping nearly 100% of your income for yourself while your neighbor goes without, you are disobeying Jesus Christ and rejecting your duty as a Christian. It doesn't matter what Bill Gates is doing. Don't worry about him. His money is none of your concern. You have your own money, don't you? You live comfortably, in relative luxury, while the homeless freeze to death on the streets. Stop blaming "the rich" for this problem and go out and do something about it, you hypocrites.
Now, why does Jesus advocate personal charity rather than government charity? Why does he put the onus on us as individuals instead of the State? I think the reason is this: love. The goal is not to eradicate poverty, like poverty is some kind of disease. The goal is simply to love each other. This is why Christ especially commends the old woman at the temple who gave comparatively little. It was, for her, an act of great love. And that is what Christ wants from us. He wants us to love each other. There is no love in the Welfare System. There is no love in taxation. It is bureaucratic, impersonal, disinterested, dehumanizing. A man is not experiencing the fruits of love when he cashes a monthly check sent to him by some government office. Rather, he is being treated like a number, a statistic, a problem that must be solved. This does not appear to be what Jesus had in mind.