The vast majority of homeless/unhoused people are completely normal healthy adults that had one bad turn in life and could not get back.
In a 2016 Census, only about 12% of the homeless population aged 15 and up were actually unable to work due to various maladies[0]. According to the same census report a whopping 62% of homeless males were currently employed.
The issue is not to just remember the 3 or 4 homeless people you've seen clearly dazed and likely unable to work, it's the thousands of people living in their car because rent is unaffordable for their income. That's the first point, abundance of housing lowers rents to the point of being affordable to Minimum-Wage workers.
Secondly, one of the first issues homeless shelters noticed is that employers require and address to even apply. So if one of those people living in their cars or under a bridge and still heading to work god forbid loses their job, they literally cannot apply to another one without a fixed address, another way affordable/abundant housing explicitly affects homeless employment.
The 12% that cannot work should probably not be on the street and should be cared for in shelters, but many shelters are filled with people who's employers underpay or pay an unlivable income and so also require shelters. Abundant housing thus allows people in the work-force to not be priced out of a roof, opening up shelters for those that cannot care for themselves.
More housing is a win-win-win. Except maybe it means aunt Karen notices more busses, which she doesn't like the sound of, hence no more developments to appease those with the ability to make their points to local government, at the cost of those that many people even avoid eye contact with.
[0] https://www.cso.ie/en/releasesandpublications/ep/p-cp5hpi/cp...