If it wasn't cheaper, their would still be an argument to be made in favor of wethouses because it seems to be far more humane than allowing people to rot away on the streets. But then the debate would be whether or not society should have to bear the cost of their poor decisions. In fact, they will have a cost to society no matter what. It just so happens that the best thing for them is also the cheapest thing for society, so there is no possible objection. So the argument goes.
No one is saying, "Do it because it's cheaper." They're saying, "Don't not do it because it's more expensive, because it isn't -- it's cheaper."