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If every church houses two homeless people, no more homeless people.
Assuming the distribution is the same for both
(it’s not)
But the point is not invalid. It’s a problem that seems insurmountable but can definitely be tackled.
Although homeless people absolutely can and do migrate. They prefer cities for somewhat similar reasons to everyone else, and with no place they are allowed to live why not squat somewhere with lots of (begging/stealing/dumpsterdiving) opportunities and shorter walks?