Although first of all.... Jesus plainly says we will never get rid of poverty.
We will always have the poor, in His words. It was said so offhandedly and casually as if the sky was blue that it is inarguable.
However. We are still required to love as Jesus loved.
I argue theologically that the point of feeding the hungry is less to eliminate hunger for the sake of the hungry but to demonstrate Christ's love.
Meaning that the reason for charity is less that the poor need charity but that people are poor so we have people to be charitable to.
We exist to love and worship after all.
Human deficiencies are caused by sin. But the reason God simply doesn't supernaturally feed them or erase our ills is also because of the free will that led to sin and deficiencies. We're supposed to demonstrate the love of Christ of our own free will.
Now the Church used to be a helpful organized entity and for the most part it still is.