Earlier quoted context omitted.
Homeless shelters still exist too. It's not about what to call it, it's about whether people are forced to be there.
If homeless shelters are shitholes, neglected, understaffed, with indifferent and uncaring (or abusing) personnel, with no boundaries between the inmates, so that dangerous and unstable people make it hell for the more well adjusted homeless people living there without recourse, then many or most homeless are not going to want to stay there.
If we see that someone in freezing weather prefers sleeping outside to sleeping in a homeless shelter, we're forced to reckon with the fact that homeless shelters must be terrible.
If we lock this person up in an equally terrible asylum, we can ignore that.