And those government services would be completely unnecessary in a free and prosperous economy where everyone can find meaningful work and pay their own way. On that same note, if my aunt had balls, she’d be my uncle. We could conjure any number of progressively more ideal hypothetical worlds, but we don’t live in any of those. The fact remains that people fall through the cracks wherever you go. France has high taxes too, and you still see homeless people in Paris. Thankfully, some people other than governments concern themselves with these worldly needs and try to help.
Governments can extract tax; churches cannot extract tithes. If there was broad-base political will to do so then the government could easily absorb such services and collect the tax, so where is the political will? If we believe the notion you put forward, Americans lack the political will to empower their government to fix the problems because such money is earmarked for religious spending. That doesn’t make a lot of sense. It makes even less sense when you consider the large overlap of religious groups and social justice-minded voters. For example, for decades most of the political will for Democrat social programs was driven by a Northern Catholic base urged to vote their conscience. Are they now voting their conscience to save the money they need to act to cover the inaction of the government that could do the job if they just voted their conscience?
I would propose a much simpler answer: most Americans just don’t care, and the those who do don’t trust the government to properly spend money that they could spend directly.