I feel like the disconnect is that Nixon, the civil rights movement, etc has soured people on the idea that the government is "the people" but instead an adversarial entity. There is nothing more possible of providing for helping your fellow man than the state when the people are empowered and engaged in their government. I don't think churches alone can do it. If the church had a solution for the sick and impoverished then I guess I missed it. I don't think businesses or individuals can do it. Not so long as businesses have fiduciary responsibility to their stakeholders can a business do things with purely the good of the people in mind. Individuals lack the capital to do so and the ones who have been shaping laws to horde capital have been doing it to squirrel away money for the ecological hellscape future for themselves not to help the public.
Where do you think the government gets it funding from in the first place? From the people and businesses, of course.
I'm not suggesting the government doesn't help people, nor am I suggesting it is evil or bad, but I will submit that there's no way it's as efface went as someone giving directly to someone in need.
Would the needs be met at the same level the government provides them? I'll further submit there's no way to know either way.
Ultimately, the point is that forced giving isn't compassion, but as the US is the most giving nation on the planet, I'll humbly submit that those in need would still be helped if the middle man (with his additional costs) was removed.