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Funnily, it is demonstrably not cheaper. Study after study shows its not cheaper. But its not about what costs the state the least, its about making sure wealth protects you from suffering.
Same with healthcare. We pay, what, 4x more for our healthcare system than the next highest country that has universal healthcare? It doesn’t matter. Our system continues to funnel the money upward and punish the poor as well as further entrench them in poverty. America is lovely.