Really if you want to stop the homeless from living "on the street" you've got to, if anything keep the laws about sleeping in public, create some system to coordinate the homeless to get to the shelters, like say, some bus stops with a bus driver who drives people around to the right shelters... and come up with a looser system of checking in and out but not too lose to avoid letting in people while drunk or high.
and that'd cover most of it, though you'd still have issues from things like general threat of injury and sickness/shelters splitting up families.
Really though, like i said, it's really only the chronic homeless who have a serious problem... which, transitory homes work much better for them and they're the ones taking up like 60-80% of the resources.
Which is what is generally already being done.
